User:Polygon/Collection of BB Champions: Difference between revisions
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(Completed list of Champions for Oracle Busy Beaver Lambda) |
(Used more efficient formatting) |
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| Line 10: | Line 10: | ||
|- | |- | ||
|BB(1) | |BB(1) | ||
|<math> 1 </math> | |<math>1</math> | ||
|{{TM|1RZ---|halt}} | |{{TM|1RZ---|halt}} | ||
|- | |- | ||
|[[BB(2)]] | |[[BB(2)]] | ||
|<math> 6 </math> | |<math>6</math> | ||
|{{TM|1RB1LB_1LA1RZ|halt}} {{TM|1RB0LB_1LA1RZ|halt}} {{TM|1RB1RZ_1LB1LA|halt}} {{TM|1RB1RZ_0LB1LA|halt}} {{TM|0RB1RZ_1LA1RB|halt}} | |{{TM|1RB1LB_1LA1RZ|halt}} {{TM|1RB0LB_1LA1RZ|halt}} {{TM|1RB1RZ_1LB1LA|halt}} {{TM|1RB1RZ_0LB1LA|halt}} {{TM|0RB1RZ_1LA1RB|halt}} | ||
|- | |- | ||
|[[BB(3)]] | |[[BB(3)]] | ||
|<math> 21 </math> | |<math>21</math> | ||
|{{TM|1RB1RZ_1LB0RC_1LC1LA|halt}} | |{{TM|1RB1RZ_1LB0RC_1LC1LA|halt}} | ||
|- | |- | ||
|[[BB(4)]] | |[[BB(4)]] | ||
|<math> 107 </math> | |<math>107</math> | ||
|{{TM|1RB1LB_1LA0LC_1RZ1LD_1RD0RA|halt}} | |{{TM|1RB1LB_1LA0LC_1RZ1LD_1RD0RA|halt}} | ||
|- | |- | ||
|[[BB(5)]] | |[[BB(5)]] | ||
|<math> 47\,176\,870 </math> | |<math>47\,176\,870</math> | ||
|{{TM|1RB1LC_1RC1RB_1RD0LE_1LA1LD_1RZ0LA|halt}} | |{{TM|1RB1LC_1RC1RB_1RD0LE_1LA1LD_1RZ0LA|halt}} | ||
|- | |- | ||
|[[BB(6)]] | |[[BB(6)]] | ||
|<math> > 2\uparrow\uparrow 2\uparrow\uparrow 2\uparrow\uparrow 10 </math> | |<math>> 2\uparrow\uparrow 2\uparrow\uparrow 2\uparrow\uparrow 10</math> | ||
|{{TM|1RB1RA_1RC1RZ_1LD0RF_1RA0LE_0LD1RC_1RA0RE|halt}} | |{{TM|1RB1RA_1RC1RZ_1LD0RF_1RA0LE_0LD1RC_1RA0RE|halt}} | ||
|- | |- | ||
| Line 42: | Line 42: | ||
|- | |- | ||
|BB(9) | |BB(9) | ||
|<math> > f_\omega(f_9(2)) </math> | |<math>> f_\omega(f_9(2))</math> | ||
|{{TM|1RB1RA_0LC0LF_0RD1LC_1RA1RG_1RZ0RA_1LB1LF_1LH1RE_0LI1LH_1LB0LH|halt}} | |{{TM|1RB1RA_0LC0LF_0RD1LC_1RA1RG_1RZ0RA_1LB1LF_1LH1RE_0LI1LH_1LB0LH|halt}} | ||
|- | |- | ||
|BB(10) | |BB(10) | ||
|<math> > f_\omega^2(25) </math> | |<math>> f_\omega^2(25)</math> | ||
|{{TM|1RB1RA_0LC0LF_0RD1LC_1RA1RG_1RZ0RA_1LB1LF_1LH1RE_0LI1LH_0LF0LJ_1LH0LJ|halt}} | |{{TM|1RB1RA_0LC0LF_0RD1LC_1RA1RG_1RZ0RA_1LB1LF_1LH1RE_0LI1LH_0LF0LJ_1LH0LJ|halt}} | ||
|- | |- | ||
|BB(11) | |BB(11) | ||
|<math> > f_\omega^2(2 \uparrow\uparrow 12) > f_\omega^2(f_3(9)) </math> | |<math>> f_\omega^2(2 \uparrow\uparrow 12) > f_\omega^2(f_3(9))</math> | ||
|{{TM|1LH1LA_1LI1RG_0RD1LC_0RF1RE_1LJ0RF_1RB1RF_0LC1LH_0LC0LA_1LK1LJ_1RZ0LI_0LD1LE|halt}} | |{{TM|1LH1LA_1LI1RG_0RD1LC_0RF1RE_1LJ0RF_1RB1RF_0LC1LH_0LC0LA_1LK1LJ_1RZ0LI_0LD1LE|halt}} | ||
|- | |- | ||
|BB(12) | |BB(12) | ||
|<math> > f_\omega^4(2 \uparrow\uparrow\uparrow 4-3) > f_\omega^4(f_4(2)) </math> | |<math>> f_\omega^4(2 \uparrow\uparrow\uparrow 4-3) > f_\omega^4(f_4(2))</math> | ||
|{{TM|0LJ0RF_1LH1RC_0LD0LG_0RE1LD_1RF1RA_1RB1RF_1LC1LG_1LL1LI_1LK0LH_1RH1LJ_1RZ1LA_1RF1LL|halt}} | |{{TM|0LJ0RF_1LH1RC_0LD0LG_0RE1LD_1RF1RA_1RB1RF_1LC1LG_1LL1LI_1LK0LH_1RH1LJ_1RZ1LA_1RF1LL|halt}} | ||
|- | |- | ||
|BB(14) | |BB(14) | ||
|<math> > f_{\omega + 1}(65\,536) > g_{64} </math> | |<math>> f_{\omega + 1}(65\,536) > g_{64}</math> | ||
|{{TM|1LH1LA_1LI1RG_0RD1LC_0RF1RE_1LJ0RF_1RB1RF_0LC1LH_0LC0LA_1LK1LJ_1RL0LI_0LL1LE_1LM1RZ_0LN1LF_0LJ---|halt}} | |{{TM|1LH1LA_1LI1RG_0RD1LC_0RF1RE_1LJ0RF_1RB1RF_0LC1LH_0LC0LA_1LK1LJ_1RL0LI_0LL1LE_1LM1RZ_0LN1LF_0LJ---|halt}} | ||
|- | |- | ||
|BB(15) | |BB(15) | ||
|<math> > f_{\omega + 1}(f_\omega(10^{57})) </math> | |<math>> f_{\omega + 1}(f_\omega(10^{57}))</math> | ||
|{{TM|0RH1LD_1RI0RC_1RB1LD_0LD1LE_1LF1RA_1RG0LE_1RB1RG_1RD1RA_0LN0RJ_1RZ0LK_0LK1LL_1RG1LM_0LL0LL_1LO1LN_0LG1LN|halt}} | |{{TM|0RH1LD_1RI0RC_1RB1LD_0LD1LE_1LF1RA_1RG0LE_1RB1RG_1RD1RA_0LN0RJ_1RZ0LK_0LK1LL_1RG1LM_0LL0LL_1LO1LN_0LG1LN|halt}} | ||
|- | |- | ||
|BB(16) | |BB(16) | ||
|<math> > f_{\omega + 1}^2(10^{10^{57}}) </math> | |<math>> f_{\omega + 1}^2(10^{10^{57}})</math> | ||
| | | | ||
|- | |- | ||
|BB(18) | |BB(18) | ||
|<math> > f_{\omega + 2}(f_{\omega + 1}^3(f_{\omega}^2(60))) </math> | |<math>> f_{\omega + 2}(f_{\omega + 1}^3(f_{\omega}^2(60)))</math> | ||
| | | | ||
|- | |- | ||
|BB(20) | |BB(20) | ||
|<math> > f_{\omega + 2}^2(21) </math> | |<math>> f_{\omega + 2}^2(21)</math> | ||
| | | | ||
|- | |- | ||
|BB(21) | |BB(21) | ||
|<math> > f_{\omega^2}^2(4 \uparrow\uparrow 341) </math> | |<math>> f_{\omega^2}^2(4 \uparrow\uparrow 341)</math> | ||
| | | | ||
|- | |- | ||
|BB(40) | |BB(40) | ||
|<math> > f_{\omega^\omega}(75\,500) </math> | |<math>> f_{\omega^\omega}(75\,500)</math> | ||
| | | | ||
|- | |- | ||
|BB(41) | |BB(41) | ||
|<math> > f_{\omega^\omega}^4(32) </math> | |<math>> f_{\omega^\omega}^4(32)</math> | ||
| | | | ||
|- | |- | ||
|BB(51) | |BB(51) | ||
|<math> > f_{\varepsilon_0 + 1}(8) </math> | |<math>> f_{\varepsilon_0 + 1}(8)</math> | ||
| | | | ||
|} | |} | ||
| Line 101: | Line 101: | ||
|- | |- | ||
|BB(1,3) | |BB(1,3) | ||
|<math> 1 </math> | |<math>1</math> | ||
|{{TM|1RZ------|halt}} | |{{TM|1RZ------|halt}} | ||
|- | |- | ||
|[[BB(2,3)]] | |[[BB(2,3)]] | ||
|<math> 38 </math> | |<math>38</math> | ||
|{{TM|1RB2LB1RZ_2LA2RB1LB|halt}} | |{{TM|1RB2LB1RZ_2LA2RB1LB|halt}} | ||
|- | |- | ||
|[[BB(3,3)]] | |[[BB(3,3)]] | ||
|<math> \geq 119\,112\,334\,170\,342\,541 > 10^{17} </math> | |<math>\geq 119\,112\,334\,170\,342\,541 > 10^{17}</math> | ||
|{{TM|0RB2LA1RA_1LA2RB1RC_1RZ1LB1LC|halt}} | |{{TM|0RB2LA1RA_1LA2RB1RC_1RZ1LB1LC|halt}} | ||
|- | |- | ||
|[[BB(4,3)]] | |[[BB(4,3)]] | ||
|<math> > 2 \uparrow\uparrow\uparrow (2^{2^{32}+1}-1)</math> | |<math>> 2 \uparrow\uparrow\uparrow (2^{2^{32}+1}-1)</math> | ||
|{{TM|0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD|halt}} | |{{TM|0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD|halt}} | ||
|} | |} | ||
| Line 124: | Line 124: | ||
|- | |- | ||
|BB(1,4) | |BB(1,4) | ||
|<math> 1 </math> | |<math>1</math> | ||
|{{TM|1RZ---------|halt}} | |{{TM|1RZ---------|halt}} | ||
|- | |- | ||
|[[BB(2,4)]] | |[[BB(2,4)]] | ||
|<math> 3\,932\,964 </math> | |<math>3\,932\,964</math> | ||
|{{TM|1RB2LA1RA1RA_1LB1LA3RB1RZ|halt}} | |{{TM|1RB2LA1RA1RA_1LB1LA3RB1RZ|halt}} | ||
|- | |- | ||
|BB(3,4) | |BB(3,4) | ||
|<math> > 2 \uparrow^{15} 5 </math> | |<math>> 2 \uparrow^{15} 5</math> | ||
|{{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}} | |{{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}} | ||
|} | |} | ||
| Line 143: | Line 143: | ||
|- | |- | ||
|BB(1,5) | |BB(1,5) | ||
|<math> 1 </math> | |<math>1</math> | ||
|{{TM|1RZ------------|halt}} | |{{TM|1RZ------------|halt}} | ||
|- | |- | ||
|[[BB(2,5)]] | |[[BB(2,5)]] | ||
|<math> > 10^{10^{10^{3\,314\,360}}} </math> | |<math>> 10^{10^{10^{3\,314\,360}}}</math> | ||
|{{TM|1RB3LA4RB0RB2LA_1LB2LA3LA1RA1RZ|halt}} | |{{TM|1RB3LA4RB0RB2LA_1LB2LA3LA1RA1RZ|halt}} | ||
|- | |- | ||
|BB(3,5) | |BB(3,5) | ||
|<math> > f_\omega(2 \uparrow^{15} 5) > f_\omega^2(15) </math> | |<math>> f_\omega(2 \uparrow^{15} 5) > f_\omega^2(15)</math> | ||
|{{TM|1RB3LB4LC2RA4LB_2LC3RB1LC2RA1RZ_3RB1LB3LC2RC4LC|halt}} | |{{TM|1RB3LB4LC2RA4LB_2LC3RB1LC2RA1RZ_3RB1LB3LC2RC4LC|halt}} | ||
|} | |} | ||
| Line 162: | Line 162: | ||
|- | |- | ||
|BB(1,6) | |BB(1,6) | ||
|<math> 1 </math> | |<math>1</math> | ||
|{{TM|1RZ---------------|halt}} | |{{TM|1RZ---------------|halt}} | ||
|- | |- | ||
|BB(2,6) | |BB(2,6) | ||
|<math> > 10 \uparrow\uparrow 10 \uparrow\uparrow 10^{10^{115}} </math> | |<math>> 10 \uparrow\uparrow 10 \uparrow\uparrow 10^{10^{115}}</math> | ||
|{{TM|1RB3RB5RA1LB5LA2LB_2LA2RA4RB1RZ3LB2LA|halt}} | |{{TM|1RB3RB5RA1LB5LA2LB_2LA2RA4RB1RZ3LB2LA|halt}} | ||
|} | |} | ||
| Line 178: | Line 178: | ||
|- | |- | ||
|Σ(1) | |Σ(1) | ||
|<math> 1 </math> | |<math>1</math> | ||
|{{TM|1RZ---|halt}} | |{{TM|1RZ---|halt}} | ||
|- | |- | ||
|Σ(2) | |Σ(2) | ||
|<math> 4 </math> | |<math>4</math> | ||
|{{TM|1RB1LB_1LA1RZ|halt}} | |{{TM|1RB1LB_1LA1RZ|halt}} | ||
|- | |- | ||
|Σ(3) | |Σ(3) | ||
|<math> 6 </math> | |<math>6</math> | ||
|{{TM|1RB1RZ_0RC1RB_1LC1LA|halt}} {{TM|1RB1RC_1LC1RZ_1RA0LB|halt}} {{TM|1RB1LC_1LA1RB_1LB1RZ|halt}} {{TM|1RB1RA_1LC1RZ_1RA1LB|halt}} {{TM|1RB1LC_1RC1RZ_1LA0LB|halt}} | |{{TM|1RB1RZ_0RC1RB_1LC1LA|halt}} {{TM|1RB1RC_1LC1RZ_1RA0LB|halt}} {{TM|1RB1LC_1LA1RB_1LB1RZ|halt}} {{TM|1RB1RA_1LC1RZ_1RA1LB|halt}} {{TM|1RB1LC_1RC1RZ_1LA0LB|halt}} | ||
|- | |- | ||
|Σ(4) | |Σ(4) | ||
|<math> 13 </math> | |<math>13</math> | ||
|{{TM|1RB1LB_1LA0LC_1RZ1LD_1RD0RA|halt}} {{TM|1RB0RC_1LA1RA_1RZ1RD_1LD0LB|halt}} | |{{TM|1RB1LB_1LA0LC_1RZ1LD_1RD0RA|halt}} {{TM|1RB0RC_1LA1RA_1RZ1RD_1LD0LB|halt}} | ||
|- | |- | ||
|Σ(5) | |Σ(5) | ||
|<math> 4098 </math> | |<math>4098</math> | ||
|{{TM|1RB1LC_1RC1RB_1RD0LE_1LA1LD_1RZ0LA|halt}} {{TM|1RB1RA_1LC1LB_1RA1LD_1RA1LE_1RZ0LC|halt}} | |{{TM|1RB1LC_1RC1RB_1RD0LE_1LA1LD_1RZ0LA|halt}} {{TM|1RB1RA_1LC1LB_1RA1LD_1RA1LE_1RZ0LC|halt}} | ||
|- | |- | ||
|Σ(6) | |Σ(6) | ||
|<math> > 2\uparrow\uparrow 2\uparrow\uparrow 2\uparrow\uparrow 10 </math> | |<math>> 2\uparrow\uparrow 2\uparrow\uparrow 2\uparrow\uparrow 10</math> | ||
|{{TM|1RB1RA_1RC1RZ_1LD0RF_1RA0LE_0LD1RC_1RA0RE|halt}} | |{{TM|1RB1RA_1RC1RZ_1LD0RF_1RA0LE_0LD1RC_1RA0RE|halt}} | ||
|- | |- | ||
| Line 213: | Line 213: | ||
|- | |- | ||
|Σ(1,3) | |Σ(1,3) | ||
|<math> 1 </math> | |<math>1</math> | ||
|{{TM|1RZ------|halt}} | |{{TM|1RZ------|halt}} | ||
|- | |- | ||
|Σ(2,3) | |Σ(2,3) | ||
|<math> 9 </math> | |<math>9</math> | ||
|{{TM|1RB2LB1RZ_2LA2RB1LB|halt}} | |{{TM|1RB2LB1RZ_2LA2RB1LB|halt}} | ||
|- | |- | ||
|Σ(3,3) | |Σ(3,3) | ||
|<math> \geq 374\,676\,383 </math> | |<math>\geq 374\,676\,383</math> | ||
|{{TM|0RB2LA1RA_1LA2RB1RC_1RZ1LB1LC|halt}} | |{{TM|0RB2LA1RA_1LA2RB1RC_1RZ1LB1LC|halt}} | ||
|- | |- | ||
|Σ(4,3) | |Σ(4,3) | ||
|<math> > 2 \uparrow\uparrow\uparrow 2^{2^{32}}</math> | |<math>> 2 \uparrow\uparrow\uparrow 2^{2^{32}}</math> | ||
|{{TM|0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD|halt}} | |{{TM|0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD|halt}} | ||
|} | |} | ||
| Line 236: | Line 236: | ||
|- | |- | ||
|Σ(1,4) | |Σ(1,4) | ||
|<math> 1 </math> | |<math>1</math> | ||
|{{TM|1RZ---------|halt}} | |{{TM|1RZ---------|halt}} | ||
|- | |- | ||
|Σ(2,4) | |Σ(2,4) | ||
|<math> 2050 </math> | |<math>2050</math> | ||
|{{TM|1RB2LA1RA1RA_1LB1LA3RB1RZ|halt}} | |{{TM|1RB2LA1RA1RA_1LB1LA3RB1RZ|halt}} | ||
|} | |} | ||
| Line 251: | Line 251: | ||
|- | |- | ||
|Σ(1,5) | |Σ(1,5) | ||
|<math> 1 </math> | |<math>1</math> | ||
|{{TM|1RZ------------|halt}} | |{{TM|1RZ------------|halt}} | ||
|- | |- | ||
|Σ(2,5) | |Σ(2,5) | ||
|<math> > 10^{10^{10^{3\,314\,360}}} </math> | |<math>> 10^{10^{10^{3\,314\,360}}}</math> | ||
|{{TM|1RB3LA4RB0RB2LA_1LB2LA3LA1RA1RZ|halt}} | |{{TM|1RB3LA4RB0RB2LA_1LB2LA3LA1RA1RZ|halt}} | ||
|} | |} | ||
| Line 268: | Line 268: | ||
|- | |- | ||
|BBB(1) | |BBB(1) | ||
|<math> 1 </math> | |<math>1</math> | ||
| | | | ||
|- | |- | ||
|BBB(2) | |BBB(2) | ||
|<math> 6 </math> | |<math>6</math> | ||
| | | | ||
|- | |- | ||
|BBB(3) | |BBB(3) | ||
|<math> 55 </math> | |<math>55</math> | ||
|{{TM|1LB0RB_1RA0LC_1RC1RA}} | |{{TM|1LB0RB_1RA0LC_1RC1RA}} | ||
|- | |- | ||
|BBB(4) | |BBB(4) | ||
|<math> \geq 32\,779\,478 </math> | |<math>\geq 32\,779\,478</math> | ||
| | | | ||
|- | |- | ||
|BBB(5) | |BBB(5) | ||
|<math> \geq 10^{14006} </math> | |<math>\geq 10^{14006}</math> | ||
| | | | ||
|} | |} | ||
| Line 303: | Line 303: | ||
|- | |- | ||
|BBB(3,3) | |BBB(3,3) | ||
|<math> \geq 10 \uparrow\uparrow 6 </math> | |<math>\geq 10 \uparrow\uparrow 6</math> | ||
| | | | ||
|} | |} | ||
| Line 317: | Line 317: | ||
|- | |- | ||
|num(1) | |num(1) | ||
|<math> 1 </math> | |<math>1</math> | ||
|{{TM|1RZ---|halt}} | |{{TM|1RZ---|halt}} | ||
|- | |- | ||
|num(2) | |num(2) | ||
|<math> 4 </math> | |<math>4</math> | ||
|{{TM|1RB1LB_1LA1LZ|halt}} | |{{TM|1RB1LB_1LA1LZ|halt}} | ||
|- | |- | ||
|num(3) | |num(3) | ||
|<math> 6 </math> | |<math>6</math> | ||
|{{TM|1RB1LC_1RC1LZ_1LA0LB|halt}} | |{{TM|1RB1LC_1RC1LZ_1LA0LB|halt}} | ||
|- | |- | ||
|num(4) | |num(4) | ||
|<math> 12 </math> | |<math>12</math> | ||
|{{TM|1RB0LA_1RC1LB_1LB1RD_1RZ0RA|halt}} | |{{TM|1RB0LA_1RC1LB_1LB1RD_1RZ0RA|halt}} | ||
|- | |- | ||
|num(5) | |num(5) | ||
|<math> 165 </math> | |<math>165</math> | ||
|{{TM|1RB1LA_1RC1LE_1RD1RE_0LA1RC_1RZ0LB|halt}} {{TM|0RB1LD_1LC1RB_1LD1RE_1LA1LE_1LZ0RC|halt}} | |{{TM|1RB1LA_1RC1LE_1RD1RE_0LA1RC_1RZ0LB|halt}} {{TM|0RB1LD_1LC1RB_1LD1RE_1LA1LE_1LZ0RC|halt}} | ||
|} | |} | ||
| Line 345: | Line 345: | ||
|- | |- | ||
|BBi(1) | |BBi(1) | ||
|<math> 1 </math> | |<math>1</math> | ||
|{{TM|0RH|halt}} {{TM|1RH---|halt}} | |{{TM|0RH|halt}} {{TM|1RH---|halt}} | ||
|- | |- | ||
|BBi(2) | |BBi(2) | ||
|<math> 3 </math> | |<math>3</math> | ||
|{{TM|0RB---_1LA---|halt}} | |{{TM|0RB---_1LA---|halt}} | ||
|- | |- | ||
|BBi(3) | |BBi(3) | ||
|<math> 5 </math> | |<math>5</math> | ||
|{{TM|1RB1LB_1LA---|halt}} | |{{TM|1RB1LB_1LA---|halt}} | ||
|- | |- | ||
|BBi(4) | |BBi(4) | ||
|<math> 16 </math> | |<math>16</math> | ||
|{{TM|1RB---_0RC---_1LC0LA|halt}} | |{{TM|1RB---_0RC---_1LC0LA|halt}} | ||
|- | |- | ||
|BBi(5) | |BBi(5) | ||
|<math> 37 </math> | |<math>37</math> | ||
|{{TM|1RB2LB---_2LA2RB1LB|halt}} | |{{TM|1RB2LB---_2LA2RB1LB|halt}} | ||
|- | |- | ||
|BBi(6) | |BBi(6) | ||
|<math> 123 </math> | |<math>123</math> | ||
|{{TM|1RB3LA1RA0LA_2LA------3RA|halt}} | |{{TM|1RB3LA1RA0LA_2LA------3RA|halt}} | ||
|- | |- | ||
|BBi(7) | |BBi(7) | ||
|<math> 3\,932\,963 </math> | |<math>3\,932\,963</math> | ||
|{{TM|1RB2LA1RA1RA_1LB1LA3RB---|halt}} {{TM|1RB2LA1RA_1LC1LA2RB_---1LA---|halt}} | |{{TM|1RB2LA1RA1RA_1LB1LA3RB---|halt}} {{TM|1RB2LA1RA_1LC1LA2RB_---1LA---|halt}} | ||
|- | |- | ||
|BBi(8) | |BBi(8) | ||
|<math> >6.889 \times 10^{1565} </math> | |<math>>6.889 \times 10^{1565}</math> | ||
|{{TM|1RB1LA------_1RC3LB1RB---_2LA2LC---0LC|halt}} | |{{TM|1RB1LA------_1RC3LB1RB---_2LA2LC---0LC|halt}} | ||
|} | |} | ||
| Line 384: | Line 384: | ||
|- | |- | ||
|Σi(1) | |Σi(1) | ||
|<math> 1 </math> | |<math>1</math> | ||
|{{TM|1RH---|halt}} | |{{TM|1RH---|halt}} | ||
|- | |- | ||
|Σi(2) | |Σi(2) | ||
|<math> 2 </math> | |<math>2</math> | ||
|{{TM|1RB---_1LA---|halt}} | |{{TM|1RB---_1LA---|halt}} | ||
|- | |- | ||
|Σi(3) | |Σi(3) | ||
|<math> 4 </math> | |<math>4</math> | ||
|{{TM|1RB1LB_1LA---|halt}} | |{{TM|1RB1LB_1LA---|halt}} | ||
|- | |- | ||
|Σi(4) | |Σi(4) | ||
|<math> 5 </math> | |<math>5</math> | ||
|{{TM|1RB0LB---_1LA2RA---|halt}} | |{{TM|1RB0LB---_1LA2RA---|halt}} | ||
|- | |- | ||
|Σi(5) | |Σi(5) | ||
|<math> 9 </math> | |<math>9</math> | ||
|{{TM|1RB2LB---_2LA2RB1LB|halt}} | |{{TM|1RB2LB---_2LA2RB1LB|halt}} | ||
|- | |- | ||
|Σi(6) | |Σi(6) | ||
|<math> 14 </math> | |<math>14</math> | ||
|{{TM|1RB3LA1RA0LA_2LA------3RA|halt}} | |{{TM|1RB3LA1RA0LA_2LA------3RA|halt}} | ||
|- | |- | ||
|Σi(7) | |Σi(7) | ||
|<math> 2050 </math> | |<math>2050</math> | ||
|{{TM|1RB2LA1RA1RA_1LB1LA3RB---|halt}} {{TM|1RB2LA1RA_1LC1LA2RB_---1LA---|halt}} | |{{TM|1RB2LA1RA1RA_1LB1LA3RB---|halt}} {{TM|1RB2LA1RA_1LC1LA2RB_---1LA---|halt}} | ||
|- | |- | ||
|Σi(8) | |Σi(8) | ||
|<math> >1.355 \times 10^{783} </math> | |<math>>1.355 \times 10^{783}</math> | ||
|{{TM|1RB1LA------_1RC3LB1RB---_2LA2LC---0LC|halt}} | |{{TM|1RB1LA------_1RC3LB1RB---_2LA2LC---0LC|halt}} | ||
|} | |} | ||
| Line 429: | Line 429: | ||
|- | |- | ||
|BB<sub>rev</sub>(2) | |BB<sub>rev</sub>(2) | ||
|<math> 6 </math> | |<math>6</math> | ||
|{{TM|0RB1RZ_1LA1RB|halt}} | |{{TM|0RB1RZ_1LA1RB|halt}} | ||
|- | |- | ||
|BB<sub>rev</sub>(3) | |BB<sub>rev</sub>(3) | ||
|<math> 17 </math> | |<math>17</math> | ||
|{{TM|0RB1RZ_0LC1RA_1RB1LC|halt}} | |{{TM|0RB1RZ_0LC1RA_1RB1LC|halt}} | ||
|- | |- | ||
|BB<sub>rev</sub>(4) | |BB<sub>rev</sub>(4) | ||
|<math> 48 </math> | |<math>48</math> | ||
|{{TM|1RB0LD_0LC0RB_1LA1LD_1LC1RZ|halt}} | |{{TM|1RB0LD_0LC0RB_1LA1LD_1LC1RZ|halt}} | ||
|- | |- | ||
|BB<sub>rev</sub>(5) | |BB<sub>rev</sub>(5) | ||
|<math> 388 </math> | |<math>388</math> | ||
|{{TM|1RB0RD_1RC0RB_1RD1RZ_1LE1LA_0LE0LA|halt}} | |{{TM|1RB0RD_1RC0RB_1RD1RZ_1LE1LA_0LE0LA|halt}} | ||
|- | |- | ||
|BB<sub>rev</sub>(6) | |BB<sub>rev</sub>(6) | ||
|<math> \geq 537\,556 </math> | |<math>\geq 537\,556</math> | ||
|{{TM|1RB1LD_1LC1RE_0LD0LC_0RE0RF_0RA1RZ_1RF1RA|halt}} | |{{TM|1RB1LD_1LC1RE_0LD0LC_0RE0RF_0RA1RZ_1RF1RA|halt}} | ||
|- | |- | ||
|BB<sub>rev</sub>(7) | |BB<sub>rev</sub>(7) | ||
|<math> >10^{19} </math> | |<math>>10^{19}</math> | ||
|{{TM|1RB1LD_0LC0LD_1LC1LA_0LA1RE_0RF0RE_0RG1RF_0RB1RZ|halt}} | |{{TM|1RB1LD_0LC0LD_1LC1LA_0LA1RE_0RF0RE_0RG1RF_0RB1RZ|halt}} | ||
|} | |} | ||
| Line 465: | Line 465: | ||
|- | |- | ||
|Σ<sub>rev</sub>(2) | |Σ<sub>rev</sub>(2) | ||
|<math> \geq 2 </math> | |<math>\geq 2</math> | ||
|{{TM|0RB1RZ_1LA1RB|halt}} | |{{TM|0RB1RZ_1LA1RB|halt}} | ||
|- | |- | ||
|Σ<sub>rev</sub>(3) | |Σ<sub>rev</sub>(3) | ||
|<math> \geq 4 </math> | |<math>\geq 4</math> | ||
|{{TM|0RB1RZ_0LC1RA_1RB1LC|halt}} | |{{TM|0RB1RZ_0LC1RA_1RB1LC|halt}} | ||
|- | |- | ||
|Σ<sub>rev</sub>(4) | |Σ<sub>rev</sub>(4) | ||
|<math> \geq 6 </math> | |<math>\geq 6</math> | ||
|{{TM|1RB0LD_0LC0RB_1LA1LD_1LC1RZ|halt}} | |{{TM|1RB0LD_0LC0RB_1LA1LD_1LC1RZ|halt}} | ||
|- | |- | ||
|Σ<sub>rev</sub>(5) | |Σ<sub>rev</sub>(5) | ||
|<math> \geq 16 </math> | |<math>\geq 16</math> | ||
|{{TM|1RB0RD_1RC0RB_1RD1RZ_1LE1LA_0LE0LA|halt}} | |{{TM|1RB0RD_1RC0RB_1RD1RZ_1LE1LA_0LE0LA|halt}} | ||
|- | |- | ||
|Σ<sub>rev</sub>(6) | |Σ<sub>rev</sub>(6) | ||
|<math> \geq 1161 </math> | |<math>\geq 1161</math> | ||
|{{TM|1RB1LD_1LC1RE_0LD0LC_0RE0RF_0RA1RZ_1RF1RA|halt}} | |{{TM|1RB1LD_1LC1RE_0LD0LC_0RE0RF_0RA1RZ_1RF1RA|halt}} | ||
|} | |} | ||
| Line 504: | Line 504: | ||
|- | |- | ||
|BBS(3,2) | |BBS(3,2) | ||
|<math> 101 </math> | |<math>101</math> | ||
|{{TM|1RB1LB_0RC0LA_1LC0LA}} | |{{TM|1RB1LB_0RC0LA_1LC0LA}} | ||
|- | |- | ||
|BBS(4,2) | |BBS(4,2) | ||
|<math> \geq 119\,120\,230\,102 </math> | |<math>\geq 119\,120\,230\,102</math> | ||
|{{TM|1RB1LC_0LA1RD_0RB0LC_1LA0RD}} | |{{TM|1RB1LC_0LA1RD_0RB0LC_1LA0RD}} | ||
|} | |} | ||
| Line 525: | Line 525: | ||
|- | |- | ||
|BBS(2,4) | |BBS(2,4) | ||
|<math> \geq 293\,225\,660\,896 </math> | |<math>\geq 293\,225\,660\,896</math> | ||
|{{TM|1RB2LA0RA3LA_1LA1LB3RB1RA}} | |{{TM|1RB2LA0RA3LA_1LA1LB3RB1RA}} | ||
|} | |} | ||
| Line 545: | Line 545: | ||
|- | |- | ||
|BBP(3,2) | |BBP(3,2) | ||
|<math> 92 </math> | |<math>92</math> | ||
|{{TM|1RB0LA_0RC1LA_1LC0RB}} | |{{TM|1RB0LA_0RC1LA_1LC0RB}} | ||
|- | |- | ||
|BBP(4,2) | |BBP(4,2) | ||
|<math> \geq 212\,081\,736 </math> | |<math>\geq 212\,081\,736</math> | ||
|{{TM|1RB0LA_0RC1RD_1LD0RB_1LA1RB}} | |{{TM|1RB0LA_0RC1RD_1LD0RB_1LA1RB}} | ||
|} | |} | ||
| Line 566: | Line 566: | ||
|- | |- | ||
|BBP(2,4) | |BBP(2,4) | ||
|<math> \geq 33\,209\,131 </math> | |<math>\geq 33\,209\,131</math> | ||
|{{TM|1RB0RA3LB1RB_2LA0LB1RA2RB}} | |{{TM|1RB0RA3LB1RB_2LA0LB1RA2RB}} | ||
|} | |} | ||
| Line 579: | Line 579: | ||
|- | |- | ||
|BBλ(21) | |BBλ(21) | ||
|<math> 22 </math> | |<math>22</math> | ||
|<code> \(\1 1) (1 (\2)) </code> | |<code>\(\1 1) (1 (\2))</code> | ||
|- | |- | ||
|BBλ(22) | |BBλ(22) | ||
|<math> 24 </math> | |<math>24</math> | ||
|<code> \(\1 1) (1 (\\1))\(\1 1 1) (1 1) </code> | |<code>\(\1 1) (1 (\\1))\(\1 1 1) (1 1)</code> | ||
|- | |- | ||
|BBλ(23) | |BBλ(23) | ||
|<math> 26 </math> | |<math>26</math> | ||
|<code> \(\1 1) (1 (\\2)) </code> | |<code>\(\1 1) (1 (\\2))</code> | ||
|- | |- | ||
|BBλ(24) | |BBλ(24) | ||
|<math> 30 </math> | |<math>30</math> | ||
|<code> \(\1 1 1) (1 (\1)) </code> | |<code>\(\1 1 1) (1 (\1))</code> | ||
|- | |- | ||
|BBλ(25) | |BBλ(25) | ||
|<math> 42 </math> | |<math>42</math> | ||
|<code> \(\1 1) (\1 (2 1)) </code> | |<code>\(\1 1) (\1 (2 1))</code> | ||
|- | |- | ||
|BBλ(26) | |BBλ(26) | ||
|<math> 52 </math> | |<math>52</math> | ||
|<code> (\1 1) (\\2 (1 2)) </code> | |<code>(\1 1) (\\2 (1 2))</code> | ||
|- | |- | ||
|BBλ(27) | |BBλ(27) | ||
|<math> 44 </math> | |<math>44</math> | ||
|<code> \\(\1 1) (\1 (2 1)) </code> | |<code>\\(\1 1) (\1 (2 1))</code> | ||
|- | |- | ||
|BBλ(28) | |BBλ(28) | ||
|<math> 58 </math> | |<math>58</math> | ||
|<code> \(\1 1) (\1 (2 (\2)))) </code> | |<code>\(\1 1) (\1 (2 (\2))))</code> | ||
|- | |- | ||
|BBλ(29) | |BBλ(29) | ||
|<math> 223 </math> | |<math>223</math> | ||
|<code> \(\1 1) (\1 (1 (2 1))) </code> | |<code>\(\1 1) (\1 (1 (2 1)))</code> | ||
|- | |- | ||
|BBλ(30) | |BBλ(30) | ||
|<math> 160 </math> | |<math>160</math> | ||
|<code> (\1 1 1) (\\2 (1 2)) </code> and <code> (\1 (1 1)) (\\2 (1 2)) </code> | |<code>(\1 1 1) (\\2 (1 2))</code> and <code>(\1 (1 1)) (\\2 (1 2))</code> | ||
|- | |- | ||
|BBλ(31) | |BBλ(31) | ||
|<math> 267 </math> | |<math>267</math> | ||
|<code> (\1 1) (\\2 (2 (1 2))) </code> | |<code>(\1 1) (\\2 (2 (1 2)))</code> | ||
|- | |- | ||
|BBλ(32) | |BBλ(32) | ||
|<math> 298 </math> | |<math> 298 </math> | ||
|<code> \(\1 1) (\1 (1 (2 (\2)))) </code> | |<code>\(\1 1) (\1 (1 (2 (\2))))</code> | ||
|- | |- | ||
|BBλ(33) | |BBλ(33) | ||
|<math> 1812 </math> | |<math>1812</math> | ||
|<code> \(\1 1) (\1 (1 (1 (2 1)))) </code> | |<code>\(\1 1) (\1 (1 (1 (2 1))))</code> | ||
|- | |- | ||
|BBλ(34) | |BBλ(34) | ||
|<math> 327\,686 </math> | |<math>327\,686</math> | ||
|<code> (\1 1 1 1) (\\2 (2 1)) </code> and <code> (\1 (1 1) 1) (\\2 (2 1)) </code> | |<code>(\1 1 1 1) (\\2 (2 1))</code> and <code>(\1 (1 1) 1) (\\2 (2 1))</code> | ||
|- | |- | ||
|BBλ(35) | |BBλ(35) | ||
|<math> 5 \times 3^{3^{3}} +6 > 3.8 \times 10^{13} </math> | |<math>5 \times 3^{3^{3}} +6 > 3.8 \times 10^{13}</math> | ||
|<code> (\1 1 1) (\\2 (2 (2 1))) </code> | |<code>(\1 1 1) (\\2 (2 (2 1)))</code> | ||
|- | |- | ||
|BBλ(36) | |BBλ(36) | ||
|<math> 5 \times 2^{2^{2^{3}}} +6 > 5.7 \times 10^{77} </math> | |<math>5 \times 2^{2^{2^{3}}} +6 > 5.7 \times 10^{77}</math> | ||
|<code> (\1 1) (\1 (1 (\\2 (2 1)))) </code> | |<code>(\1 1) (\1 (1 (\\2 (2 1))))</code> | ||
|- | |- | ||
|BBλ(37) | |BBλ(37) | ||
| | |<math>BB \lambda(35) +2 =5 \times 3^{3^{3}} +8 > 3.8 \times 10^{13}</math> | ||
|<code> \(\1 1 1) (\\2 (2 (2 1))) </code> | |<code>\(\1 1 1) (\\2 (2 (2 1)))</code> | ||
|- | |- | ||
|BBλ(38) | |BBλ(38) | ||
|<math> \geq 5 \times 2^{2^{2^{2^{2}}}} +6 > 10^{10^{4}} </math> | |<math>\geq 5 \times 2^{2^{2^{2^{2}}}} +6 > 10^{10^{4}}</math> | ||
|<code> (\1 1 1 1 1) (\\2 (2 1)) </code> and <code> (\1 (1 1) 1 1) (\\2 (2 1)) </code> | |<code>(\1 1 1 1 1) (\\2 (2 1))</code> and <code>(\1 (1 1) 1 1) (\\2 (2 1))</code> | ||
|- | |- | ||
|BBλ(39) | |BBλ(39) | ||
|<math> \geq 5 \times 3^{3^{3^{3}}} +6 > 10^{10^{12}} </math> | |<math>\geq 5 \times 3^{3^{3^{3}}} +6 > 10^{10^{12}}</math> | ||
|<code> (\1 1 1 1) (\\2 (2 (2 1))) </code> | |<code>(\1 1 1 1) (\\2 (2 (2 1)))</code> | ||
|- | |- | ||
|BBλ(40) | |BBλ(40) | ||
|<math> > (2 \uparrow\uparrow)^{15}33 > 10 \uparrow\uparrow\uparrow 16 </math> | |<math>> (2 \uparrow\uparrow)^{15}33 > 10 \uparrow\uparrow\uparrow 16</math> | ||
|<code> (\1 1 1) (\1 (\\2 (2 1)) 1) </code> | |<code>(\1 1 1) (\1 (\\2 (2 1)) 1)</code> | ||
|- | |- | ||
|BBλ(41) | |BBλ(41) | ||
|<math> \geq 5 \times 3^{3^{85}} +6 > 10^{10^{40}} </math> | |<math>\geq 5 \times 3^{3^{85}} +6 > 10^{10^{40}}</math> | ||
|<code> (\1 (\1 1) 1) (\\2 (2 (2 1))) </code> | |<code>(\1 (\1 1) 1) (\\2 (2 (2 1)))</code> | ||
|- | |- | ||
|BBλ(42) | |BBλ(42) | ||
|<math> \geq | |<math>\geq BB \lambda(40) + 2 > (2 \uparrow\uparrow)^{15}33 > 10 \uparrow\uparrow\uparrow 16</math> | ||
|<code> \(\1 1 1) (\1 (\\2 (2 1)) 1) </code> | |<code>\(\1 1 1) (\1 (\\2 (2 1)) 1)</code> | ||
|- | |- | ||
|BBλ(43) | |BBλ(43) | ||
|<math> > 2 \uparrow\uparrow\uparrow 2 \uparrow\uparrow\uparrow 2 \uparrow\uparrow 8 </math> | |<math>> 2 \uparrow\uparrow\uparrow 2 \uparrow\uparrow\uparrow 2 \uparrow\uparrow 8</math> | ||
|<code> (\1 1) (\1 (\1 (\\2 (2 1)) 2)) </code> | |<code>(\1 1) (\1 (\1 (\\2 (2 1)) 2))</code> | ||
|- | |- | ||
|BBλ(44) | |BBλ(44) | ||
|<math> > 10 \uparrow\uparrow\uparrow 10 \uparrow\uparrow\uparrow 16 </math> | |<math>> 10 \uparrow\uparrow\uparrow 10 \uparrow\uparrow\uparrow 16</math> | ||
|<code> (\1 1 1 1) (\1 (\\2 (2 1)) 1) </code> | |<code>(\1 1 1 1) (\1 (\\2 (2 1)) 1)</code> | ||
|- | |- | ||
|BBλ(45) | |BBλ(45) | ||
|<math> \geq | |<math>\geq BB \lambda(43) + 2 > 2 \uparrow\uparrow\uparrow 2 \uparrow\uparrow\uparrow 2 \uparrow\uparrow 8</math> | ||
|<code> \(\1 1) (\1 (\1 (\\2 (2 1)) 2)) </code> | |<code>\(\1 1) (\1 (\1 (\\2 (2 1)) 2))</code> | ||
|- | |- | ||
|BBλ(46) | |BBλ(46) | ||
|<math> \geq | |<math>\geq BB \lambda(44) + 2 > 10 \uparrow\uparrow\uparrow 10 \uparrow\uparrow\uparrow 16</math> | ||
|<code> \(\1 1 1 1) (\1 (\\2 (2 1)) 1) </code> | |<code>\(\1 1 1 1) (\1 (\\2 (2 1)) 1)</code> | ||
|- | |- | ||
|BBλ(47) | |BBλ(47) | ||
| Line 687: | Line 687: | ||
|- | |- | ||
|BBλ(48) | |BBλ(48) | ||
|<math> > 10 \uparrow\uparrow\uparrow 10 \uparrow\uparrow\uparrow 10 \uparrow\uparrow\uparrow 16 </math> | |<math>> 10 \uparrow\uparrow\uparrow 10 \uparrow\uparrow\uparrow 10 \uparrow\uparrow\uparrow 16</math> | ||
|<code> (\1 1 1 1 1) (\1 (\\2 (2 1)) 1) </code> | |<code>(\1 1 1 1 1) (\1 (\\2 (2 1)) 1)</code> | ||
|- | |- | ||
|BBλ(49) | |BBλ(49) | ||
|<math> > f_{\omega+1}(\frac{2 \uparrow\uparrow 6}{2}) > \text{Grahams Number} </math> | |<math>> f_{\omega+1}(\frac{2 \uparrow\uparrow 6}{2}) > \text{Grahams Number}</math> | ||
|<code> (\1 1) (\1 (1 (\\1 2 (\\2 (2 1))))) </code> | |<code>(\1 1) (\1 (1 (\\1 2 (\\2 (2 1)))))</code> | ||
|- | |- | ||
|BBλ(1850) | |BBλ(1850) | ||
|<math> > \text{Loaders Number} </math> | |<math>> \text{Loaders Number}</math> | ||
|<code> Too large for this list </code> | |<code>Too large for this list</code> | ||
|} | |} | ||
==Oracle Busy Beaver for Lambda Calculus ([[Busy Beaver for lambda calculus#Oracle Busy Beaver|BBλ<sub>1</sub>]])== | ==Oracle Busy Beaver for Lambda Calculus ([[Busy Beaver for lambda calculus#Oracle Busy Beaver|BBλ<sub>1</sub>]])== | ||
Note that <math> f(n) = 6 + 5 \times BB \lambda(n) </math>. | Note that <math>f(n) = 6 + 5 \times BB \lambda(n)</math>. | ||
{| class="wikitable" | {| class="wikitable" | ||
|+ | |+ | ||
| Line 707: | Line 707: | ||
|- | |- | ||
|BBλ<sub>1</sub>(1) | |BBλ<sub>1</sub>(1) | ||
|<math> 0 </math> | |<math>0</math> | ||
| | | | ||
|- | |- | ||
|BBλ<sub>1</sub>(2) | |BBλ<sub>1</sub>(2) | ||
|<math> 1 </math> | |<math>1</math> | ||
|<code> 1 </code> | |<code>1</code> | ||
|- | |- | ||
|BBλ<sub>1</sub>(3) | |BBλ<sub>1</sub>(3) | ||
|<math> 0 </math> | |<math>0</math> | ||
| | | | ||
|- | |- | ||
|BBλ<sub>1</sub>(4) | |BBλ<sub>1</sub>(4) | ||
|<math> 4 </math> | |<math>4</math> | ||
|<code> \1 </code> | |<code>\1</code> | ||
|- | |- | ||
|BBλ<sub>1</sub>(5) | |BBλ<sub>1</sub>(5) | ||
|<math> 5 </math> | |<math>5</math> | ||
|<code> \2 </code> | |<code>\2</code> | ||
|- | |- | ||
|BBλ<sub>1</sub>(6) | |BBλ<sub>1</sub>(6) | ||
|<math> 6 </math> | |<math>6</math> | ||
|<code> \\1 </code> | |<code>\\1</code> | ||
|- | |- | ||
|BBλ<sub>1</sub>(7) | |BBλ<sub>1</sub>(7) | ||
|<math> 7 </math> | |<math>7</math> | ||
|<code> \\2 </code> | |<code>\\2</code> | ||
|- | |- | ||
|BBλ<sub>1</sub>(8) | |BBλ<sub>1</sub>(8) | ||
|<math> 26 </math> | |<math>26</math> | ||
|<code> 1 (\1) </code> | |<code>1 (\1)</code> | ||
|- | |- | ||
|BBλ<sub>1</sub>(9) | |BBλ<sub>1</sub>(9) | ||
|<math> 9 </math> | |<math>9</math> | ||
|<code> \\2 </code> | |<code>\\2</code> | ||
|- | |- | ||
|BBλ<sub>1</sub>(10) | |BBλ<sub>1</sub>(10) | ||
|<math> 36 </math> | |<math>36</math> | ||
|<code> 1 (\\1) </code> | |<code>1 (\\1)</code> | ||
|- | |- | ||
|BBλ<sub>1</sub>(11) | |BBλ<sub>1</sub>(11) | ||
|<math> 41 </math> | |<math>41</math> | ||
|<code> 1 (\\2) </code> | |<code>1 (\\2)</code> | ||
|- | |- | ||
|BBλ<sub>1</sub>(12) | |BBλ<sub>1</sub>(12) | ||
|<math> 266 </math> | |<math>266</math> | ||
|<code> 1 (1 (\1)) </code> | |<code>1 (1 (\1))</code> | ||
|- | |- | ||
|BBλ<sub>1</sub>(13) | |BBλ<sub>1</sub>(13) | ||
|<math> 51 </math> | |<math>51</math> | ||
|<code> 1 (\\2) </code> | |<code>1 (\\2)</code> | ||
|- | |- | ||
|BBλ<sub>1</sub>(14) | |BBλ<sub>1</sub>(14) | ||
|<math> f(36) = 25 \times 2^{2^{2^{3}}}+36 > 2.85 \times 10^{78} </math> | |<math>f(36) = 25 \times 2^{2^{2^{3}}}+36 > 2.85 \times 10^{78}</math> | ||
|<code> 1 (1 (\\1)) </code> | |<code>1 (1 (\\1))</code> | ||
|- | |- | ||
|BBλ<sub>1</sub>(15) | |BBλ<sub>1</sub>(15) | ||
|<math> f(41) \geq 25 \times 3^{3^{85}}+36 > 10^{10^{40}} </math> | |<math>f(41) \geq 25 \times 3^{3^{85}}+36 > 10^{10^{40}}</math> | ||
|<code> 1 (1 (\\2)) </code> | |<code>1 (1 (\\2))</code> | ||
|- | |- | ||
|BBλ<sub>1</sub>(16) | |BBλ<sub>1</sub>(16) | ||
|<math> f(266) </math> | |<math>f(266)</math> | ||
|<code> 1 (1 (1 (\1))) </code> | |<code>1 (1 (1 (\1)))</code> | ||
|- | |- | ||
|BBλ<sub>1</sub>(17) | |BBλ<sub>1</sub>(17) | ||
|<math> f(51) </math> | |<math>f(51)</math> | ||
|<code> 1 (1 (\\\2)) </code> | |<code>1 (1 (\\\2))</code> | ||
|- | |- | ||
|BBλ<sub>1</sub>(18) | |BBλ<sub>1</sub>(18) | ||
|<math> f^{4}(4) = f(f(266)) </math> | |<math>f^{4}(4) = f(f(266))</math> | ||
|<code> 1 (\1) 1 (\1) </code> | |<code>1 (\1) 1 (\1)</code> | ||
|- | |- | ||
|BBλ<sub>1</sub>(19) | |BBλ<sub>1</sub>(19) | ||
|<math> f^{3}(7) = f(f(41)) </math> | |<math>f^{3}(7) = f(f(41))</math> | ||
|<code> 1 (1 (1 (\\2))) </code> | |<code>1 (1 (1 (\\2)))</code> | ||
|- | |- | ||
|BBλ<sub>1</sub>(20) | |BBλ<sub>1</sub>(20) | ||
|<math> f^{6}(4) = f^{4}(266) </math> | |<math>f^{6}(4) = f^{4}(266)</math> | ||
|<code> 1 (\\1) 1 (\1) </code> | |<code>1 (\\1) 1 (\1)</code> | ||
|- | |- | ||
|BBλ<sub>1</sub>(21) | |BBλ<sub>1</sub>(21) | ||
|<math> f^{7}(4) = f^{5}(266) </math> | |<math>f^{7}(4) = f^{5}(266)</math> | ||
|<code> 1 (\\2) 1 (\1) </code> | |<code>1 (\\2) 1 (\1)</code> | ||
|- | |- | ||
|BBλ<sub>1</sub>(22) | |BBλ<sub>1</sub>(22) | ||
|<math> f^{52}(4) = f^{50}(266) </math> | |<math>f^{52}(4) = f^{50}(266)</math> | ||
|<code> 1 (1(\1)) 1(\1) </code> | |<code>1 (1(\1)) 1(\1)</code> | ||
|- | |- | ||
|BBλ<sub>1</sub>(28) | |BBλ<sub>1</sub>(28) | ||
|<math> \geq f^{BB \lambda(f^{3}(4))}(4) </math> | |<math>\geq f^{BB \lambda(f^{3}(4))}(4)</math> | ||
|<code> 1 (\1) 1 (\1) 1 (\1) </code> | |<code>1 (\1) 1 (\1) 1 (\1)</code> | ||
|} | |} | ||
='''Doodle Function ([[Doodle function|doodle]])'''= | ='''Doodle Function ([[Doodle function|doodle]])'''= | ||
| Line 809: | Line 809: | ||
|- | |- | ||
|doodle(3,2) | |doodle(3,2) | ||
|<math> \geq 487 </math> | |<math>\geq 487</math> | ||
| | | | ||
|} | |} | ||
='''Terminating Turmites ([[TT]])'''= | ='''Terminating Turmites ([[TT]])'''= | ||
There are currently no known/available Champions for this function. | There are currently no known/available Champions for this function. | ||
Revision as of 18:20, 14 August 2025
A collection of Busy Beaver Champions including Champions for BB-Adjacent functions.
Original Busy Beaver Functions
Maximum Shifts Function (BB)
2 Symbols:
| Runtime | Champions | |
|---|---|---|
| BB(1) | 1RZ--- (bbch)
| |
| BB(2) | 1RB1LB_1LA1RZ (bbch) 1RB0LB_1LA1RZ (bbch) 1RB1RZ_1LB1LA (bbch) 1RB1RZ_0LB1LA (bbch) 0RB1RZ_1LA1RB (bbch)
| |
| BB(3) | 1RB1RZ_1LB0RC_1LC1LA (bbch)
| |
| BB(4) | 1RB1LB_1LA0LC_1RZ1LD_1RD0RA (bbch)
| |
| BB(5) | 1RB1LC_1RC1RB_1RD0LE_1LA1LD_1RZ0LA (bbch)
| |
| BB(6) | 1RB1RA_1RC1RZ_1LD0RF_1RA0LE_0LD1RC_1RA0RE (bbch)
| |
| BB(7) | 1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF (bbch)
| |
| BB(8) | ||
| BB(9) | 1RB1RA_0LC0LF_0RD1LC_1RA1RG_1RZ0RA_1LB1LF_1LH1RE_0LI1LH_1LB0LH (bbch)
| |
| BB(10) | 1RB1RA_0LC0LF_0RD1LC_1RA1RG_1RZ0RA_1LB1LF_1LH1RE_0LI1LH_0LF0LJ_1LH0LJ (bbch)
| |
| BB(11) | 1LH1LA_1LI1RG_0RD1LC_0RF1RE_1LJ0RF_1RB1RF_0LC1LH_0LC0LA_1LK1LJ_1RZ0LI_0LD1LE (bbch)
| |
| BB(12) | 0LJ0RF_1LH1RC_0LD0LG_0RE1LD_1RF1RA_1RB1RF_1LC1LG_1LL1LI_1LK0LH_1RH1LJ_1RZ1LA_1RF1LL (bbch)
| |
| BB(14) | 1LH1LA_1LI1RG_0RD1LC_0RF1RE_1LJ0RF_1RB1RF_0LC1LH_0LC0LA_1LK1LJ_1RL0LI_0LL1LE_1LM1RZ_0LN1LF_0LJ--- (bbch)
| |
| BB(15) | 0RH1LD_1RI0RC_1RB1LD_0LD1LE_1LF1RA_1RG0LE_1RB1RG_1RD1RA_0LN0RJ_1RZ0LK_0LK1LL_1RG1LM_0LL0LL_1LO1LN_0LG1LN (bbch)
| |
| BB(16) | ||
| BB(18) | ||
| BB(20) | ||
| BB(21) | ||
| BB(40) | ||
| BB(41) | ||
| BB(51) |
3 Symbols:
| Runtime | Champions | |
|---|---|---|
| BB(1,3) | 1RZ------ (bbch)
| |
| BB(2,3) | 1RB2LB1RZ_2LA2RB1LB (bbch)
| |
| BB(3,3) | 0RB2LA1RA_1LA2RB1RC_1RZ1LB1LC (bbch)
| |
| BB(4,3) | 0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD (bbch)
|
4 Symbols:
| Runtime | Champions | |
|---|---|---|
| BB(1,4) | 1RZ--------- (bbch)
| |
| BB(2,4) | 1RB2LA1RA1RA_1LB1LA3RB1RZ (bbch)
| |
| BB(3,4) | 1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC (bbch)
|
5 Symbols:
| Runtime | Champions | |
|---|---|---|
| BB(1,5) | 1RZ------------ (bbch)
| |
| BB(2,5) | 1RB3LA4RB0RB2LA_1LB2LA3LA1RA1RZ (bbch)
| |
| BB(3,5) | 1RB3LB4LC2RA4LB_2LC3RB1LC2RA1RZ_3RB1LB3LC2RC4LC (bbch)
|
6 Symbols:
| Runtime | Champions | |
|---|---|---|
| BB(1,6) | 1RZ--------------- (bbch)
| |
| BB(2,6) | 1RB3RB5RA1LB5LA2LB_2LA2RA4RB1RZ3LB2LA (bbch)
|
Maximum Score Function (Σ)
2 Symbols:
| Score | Champions | |
|---|---|---|
| Σ(1) | 1RZ--- (bbch)
| |
| Σ(2) | 1RB1LB_1LA1RZ (bbch)
| |
| Σ(3) | 1RB1RZ_0RC1RB_1LC1LA (bbch) 1RB1RC_1LC1RZ_1RA0LB (bbch) 1RB1LC_1LA1RB_1LB1RZ (bbch) 1RB1RA_1LC1RZ_1RA1LB (bbch) 1RB1LC_1RC1RZ_1LA0LB (bbch)
| |
| Σ(4) | 1RB1LB_1LA0LC_1RZ1LD_1RD0RA (bbch) 1RB0RC_1LA1RA_1RZ1RD_1LD0LB (bbch)
| |
| Σ(5) | 1RB1LC_1RC1RB_1RD0LE_1LA1LD_1RZ0LA (bbch) 1RB1RA_1LC1LB_1RA1LD_1RA1LE_1RZ0LC (bbch)
| |
| Σ(6) | 1RB1RA_1RC1RZ_1LD0RF_1RA0LE_0LD1RC_1RA0RE (bbch)
| |
| Σ(7) | 1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF (bbch)
|
3 Symbols:
| Score | Champions | |
|---|---|---|
| Σ(1,3) | 1RZ------ (bbch)
| |
| Σ(2,3) | 1RB2LB1RZ_2LA2RB1LB (bbch)
| |
| Σ(3,3) | 0RB2LA1RA_1LA2RB1RC_1RZ1LB1LC (bbch)
| |
| Σ(4,3) | 0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD (bbch)
|
4 Symbols:
| Score | Champions | |
|---|---|---|
| Σ(1,4) | 1RZ--------- (bbch)
| |
| Σ(2,4) | 1RB2LA1RA1RA_1LB1LA3RB1RZ (bbch)
|
5 Symbols:
| Score | Champions | |
|---|---|---|
| Σ(1,5) | 1RZ------------ (bbch)
| |
| Σ(2,5) | 1RB3LA4RB0RB2LA_1LB2LA3LA1RA1RZ (bbch)
|
Beeping Busy Beavers
Beeping Busy Beaver (BBB)
2 Symbols:
| Steps taken | Champions | |
|---|---|---|
| BBB(1) | ||
| BBB(2) | ||
| BBB(3) | 1LB0RB_1RA0LC_1RC1RA (bbch)
| |
| BBB(4) | ||
| BBB(5) |
3 Symbols:
| Steps taken | Champions | |
|---|---|---|
| BBB(1,3) | ||
| BBB(2,3) | ||
| BBB(3,3) |
Beeping Booping Busy Beaver (BBBB)
There are currently no known/available Champions for this function.
Maximum Consecutive Ones Function (Num)
2 Symbols:
| Number of Ones | Champions | |
|---|---|---|
| num(1) | 1RZ--- (bbch)
| |
| num(2) | 1RB1LB_1LA1LZ (bbch)
| |
| num(3) | 1RB1LC_1RC1LZ_1LA0LB (bbch)
| |
| num(4) | 1RB0LA_1RC1LB_1LB1RD_1RZ0RA (bbch)
| |
| num(5) | 1RB1LA_1RC1LE_1RD1RE_0LA1RC_1RZ0LB (bbch) 0RB1LD_1LC1RB_1LD1RE_1LA1LE_1LZ0RC (bbch)
|
Instruction-Limited Busy Beaver
Maximum amount of steps (BBi)
| Steps | Champions | |
|---|---|---|
| BBi(1) | 0RH (bbch) 1RH--- (bbch)
| |
| BBi(2) | 0RB---_1LA--- (bbch)
| |
| BBi(3) | 1RB1LB_1LA--- (bbch)
| |
| BBi(4) | 1RB---_0RC---_1LC0LA (bbch)
| |
| BBi(5) | 1RB2LB---_2LA2RB1LB (bbch)
| |
| BBi(6) | 1RB3LA1RA0LA_2LA------3RA (bbch)
| |
| BBi(7) | 1RB2LA1RA1RA_1LB1LA3RB--- (bbch) 1RB2LA1RA_1LC1LA2RB_---1LA--- (bbch)
| |
| BBi(8) | 1RB1LA------_1RC3LB1RB---_2LA2LC---0LC (bbch)
|
Maximum Score (Σi)
| Score | Champions | |
|---|---|---|
| Σi(1) | 1RH--- (bbch)
| |
| Σi(2) | 1RB---_1LA--- (bbch)
| |
| Σi(3) | 1RB1LB_1LA--- (bbch)
| |
| Σi(4) | 1RB0LB---_1LA2RA--- (bbch)
| |
| Σi(5) | 1RB2LB---_2LA2RB1LB (bbch)
| |
| Σi(6) | 1RB3LA1RA0LA_2LA------3RA (bbch)
| |
| Σi(7) | 1RB2LA1RA1RA_1LB1LA3RB--- (bbch) 1RB2LA1RA_1LC1LA2RB_---1LA--- (bbch)
| |
| Σi(8) | 1RB1LA------_1RC3LB1RB---_2LA2LC---0LC (bbch)
|
Reversible Turing Machines
Maximum Shifts Function (BBrev)
2 Symbols:
| Steps | Champions | |
|---|---|---|
| BBrev(1) | ||
| BBrev(2) | 0RB1RZ_1LA1RB (bbch)
| |
| BBrev(3) | 0RB1RZ_0LC1RA_1RB1LC (bbch)
| |
| BBrev(4) | 1RB0LD_0LC0RB_1LA1LD_1LC1RZ (bbch)
| |
| BBrev(5) | 1RB0RD_1RC0RB_1RD1RZ_1LE1LA_0LE0LA (bbch)
| |
| BBrev(6) | 1RB1LD_1LC1RE_0LD0LC_0RE0RF_0RA1RZ_1RF1RA (bbch)
| |
| BBrev(7) | 1RB1LD_0LC0LD_1LC1LA_0LA1RE_0RF0RE_0RG1RF_0RB1RZ (bbch)
|
Maximum Score Function (Σrev)
2 Symbols:
| Score | Champions | |
|---|---|---|
| Σrev(1) | ||
| Σrev(2) | 0RB1RZ_1LA1RB (bbch)
| |
| Σrev(3) | 0RB1RZ_0LC1RA_1RB1LC (bbch)
| |
| Σrev(4) | 1RB0LD_0LC0RB_1LA1LD_1LC1RZ (bbch)
| |
| Σrev(5) | 1RB0RD_1RC0RB_1RD1RZ_1LE1LA_0LE0LA (bbch)
| |
| Σrev(6) | 1RB1LD_1LC1RE_0LD0LC_0RE0RF_0RA1RZ_1RF1RA (bbch)
|
Blanking Busy Beaver (BLB)
There are currently no known/available Champions for this function.
Period-oriented Busy Beavers
Busy Preperiodic Beaver (BBS)
2 Symbols:
| Preperiod | Champions | |
|---|---|---|
| BBS(1,2) | ||
| BBS(2,2) | ||
| BBS(3,2) | 1RB1LB_0RC0LA_1LC0LA (bbch)
| |
| BBS(4,2) | 1RB1LC_0LA1RD_0RB0LC_1LA0RD (bbch)
|
3 Symbols: It seems that currently no information is available for this domain.
4 Symbols:
| Preperiod | Champions | |
|---|---|---|
| BBS(1,4) | ||
| BBS(2,4) | 1RB2LA0RA3LA_1LA1LB3RB1RA (bbch)
|
Busy Periodic Beaver (BBP)
2 Symbols:
| Period | Champions | |
|---|---|---|
| BBP(1,2) | ||
| BBP(2,2) | ||
| BBP(3,2) | 1RB0LA_0RC1LA_1LC0RB (bbch)
| |
| BBP(4,2) | 1RB0LA_0RC1RD_1LD0RB_1LA1RB (bbch)
|
3 Symbols: It seems that currently no information is available for this domain.
4 Symbols:
| Period | Champions | |
|---|---|---|
| BBP(1,4) | ||
| BBP(2,4) | 1RB0RA3LB1RB_2LA0LB1RA2RB (bbch)
|
Busy Beaver for Lambda Calculus (BBλ)
Regular Busy Beaver for Lambda Calculus
For n = 0,1,2,3,5 BBλ(n) is undefined, while for the rest of BBλ(n) = n.
| BBλ(n) | Champions | |
|---|---|---|
| BBλ(21) | \(\1 1) (1 (\2))
| |
| BBλ(22) | \(\1 1) (1 (\\1))\(\1 1 1) (1 1)
| |
| BBλ(23) | \(\1 1) (1 (\\2))
| |
| BBλ(24) | \(\1 1 1) (1 (\1))
| |
| BBλ(25) | \(\1 1) (\1 (2 1))
| |
| BBλ(26) | (\1 1) (\\2 (1 2))
| |
| BBλ(27) | \\(\1 1) (\1 (2 1))
| |
| BBλ(28) | \(\1 1) (\1 (2 (\2))))
| |
| BBλ(29) | \(\1 1) (\1 (1 (2 1)))
| |
| BBλ(30) | (\1 1 1) (\\2 (1 2)) and (\1 (1 1)) (\\2 (1 2))
| |
| BBλ(31) | (\1 1) (\\2 (2 (1 2)))
| |
| BBλ(32) | \(\1 1) (\1 (1 (2 (\2))))
| |
| BBλ(33) | \(\1 1) (\1 (1 (1 (2 1))))
| |
| BBλ(34) | (\1 1 1 1) (\\2 (2 1)) and (\1 (1 1) 1) (\\2 (2 1))
| |
| BBλ(35) | (\1 1 1) (\\2 (2 (2 1)))
| |
| BBλ(36) | (\1 1) (\1 (1 (\\2 (2 1))))
| |
| BBλ(37) | \(\1 1 1) (\\2 (2 (2 1)))
| |
| BBλ(38) | (\1 1 1 1 1) (\\2 (2 1)) and (\1 (1 1) 1 1) (\\2 (2 1))
| |
| BBλ(39) | (\1 1 1 1) (\\2 (2 (2 1)))
| |
| BBλ(40) | (\1 1 1) (\1 (\\2 (2 1)) 1)
| |
| BBλ(41) | (\1 (\1 1) 1) (\\2 (2 (2 1)))
| |
| BBλ(42) | \(\1 1 1) (\1 (\\2 (2 1)) 1)
| |
| BBλ(43) | (\1 1) (\1 (\1 (\\2 (2 1)) 2))
| |
| BBλ(44) | (\1 1 1 1) (\1 (\\2 (2 1)) 1)
| |
| BBλ(45) | \(\1 1) (\1 (\1 (\\2 (2 1)) 2))
| |
| BBλ(46) | \(\1 1 1 1) (\1 (\\2 (2 1)) 1)
| |
| BBλ(47) | ||
| BBλ(48) | (\1 1 1 1 1) (\1 (\\2 (2 1)) 1)
| |
| BBλ(49) | (\1 1) (\1 (1 (\\1 2 (\\2 (2 1)))))
| |
| BBλ(1850) | Too large for this list
|
Oracle Busy Beaver for Lambda Calculus (BBλ1)
Note that .
| BBλ1(n) | Champions | |
|---|---|---|
| BBλ1(1) | ||
| BBλ1(2) | 1
| |
| BBλ1(3) | ||
| BBλ1(4) | \1
| |
| BBλ1(5) | \2
| |
| BBλ1(6) | \\1
| |
| BBλ1(7) | \\2
| |
| BBλ1(8) | 1 (\1)
| |
| BBλ1(9) | \\2
| |
| BBλ1(10) | 1 (\\1)
| |
| BBλ1(11) | 1 (\\2)
| |
| BBλ1(12) | 1 (1 (\1))
| |
| BBλ1(13) | 1 (\\2)
| |
| BBλ1(14) | 1 (1 (\\1))
| |
| BBλ1(15) | 1 (1 (\\2))
| |
| BBλ1(16) | 1 (1 (1 (\1)))
| |
| BBλ1(17) | 1 (1 (\\\2))
| |
| BBλ1(18) | 1 (\1) 1 (\1)
| |
| BBλ1(19) | 1 (1 (1 (\\2)))
| |
| BBλ1(20) | 1 (\\1) 1 (\1)
| |
| BBλ1(21) | 1 (\\2) 1 (\1)
| |
| BBλ1(22) | 1 (1(\1)) 1(\1)
| |
| BBλ1(28) | 1 (\1) 1 (\1) 1 (\1)
|
Doodle Function (doodle)
doodle(1,n) = 1 and doodle(2,n) = n
2 Symbols:
| Runtime | Champions | |
|---|---|---|
| doodle(3,2) |
Terminating Turmites (TT)
There are currently no known/available Champions for this function.