User:Polygon/Collection of BB Champions

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Original Busy Beaver Functions

Maximum Shifts Function (BB)

2 Symbols:

	Runtime	Champions
BB(1)	$1$	1RZ--- (bbch)
BB(2)	$6$	1RB1LB_1LA1RZ (bbch) 1RB0LB_1LA1RZ (bbch) 1RB1RZ_1LB1LA (bbch) 1RB1RZ_0LB1LA (bbch) 0RB1RZ_1LA1RB (bbch)
BB(3)	$21$	1RB1RZ_1LB0RC_1LC1LA (bbch)
BB(4)	$107$	1RB1LB_1LA0LC_1RZ1LD_1RD0RA (bbch)
BB(5)	$47\,176\,870$	1RB1LC_1RC1RB_1RD0LE_1LA1LD_1RZ0LA (bbch)
BB(6)	$>2\uparrow \uparrow 2\uparrow \uparrow 2\uparrow \uparrow 10$	1RB1RA_1RC1RZ_1LD0RF_1RA0LE_0LD1RC_1RA0RE (bbch)
BB(7)	$>2\uparrow ^{11}2\uparrow ^{11}3$	1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF (bbch)
BB(8)
BB(9)	$>f_{\omega }(f_{9}(2))$	1RB1RA_0LC0LF_0RD1LC_1RA1RG_1RZ0RA_1LB1LF_1LH1RE_0LI1LH_1LB0LH (bbch)
BB(10)	$>f_{\omega }^{2}(25)$	1RB1RA_0LC0LF_0RD1LC_1RA1RG_1RZ0RA_1LB1LF_1LH1RE_0LI1LH_0LF0LJ_1LH0LJ (bbch)
BB(11)	$>f_{\omega }^{2}(2\uparrow \uparrow 12)>f_{\omega }^{2}(f_{3}(9))$	1LH1LA_1LI1RG_0RD1LC_0RF1RE_1LJ0RF_1RB1RF_0LC1LH_0LC0LA_1LK1LJ_1RZ0LI_0LD1LE (bbch)
BB(12)	$>f_{\omega }^{4}(2\uparrow \uparrow \uparrow 4-3)>f_{\omega }^{4}(f_{4}(2))$	0LJ0RF_1LH1RC_0LD0LG_0RE1LD_1RF1RA_1RB1RF_1LC1LG_1LL1LI_1LK0LH_1RH1LJ_1RZ1LA_1RF1LL (bbch)
BB(14)	$>f_{\omega +1}(65\,536)>g_{64}$	1LH1LA_1LI1RG_0RD1LC_0RF1RE_1LJ0RF_1RB1RF_0LC1LH_0LC0LA_1LK1LJ_1RL0LI_0LL1LE_1LM1RZ_0LN1LF_0LJ--- (bbch)
BB(15)	$>f_{\omega +1}(f_{\omega }(10^{57}))$	0RH1LD_1RI0RC_1RB1LD_0LD1LE_1LF1RA_1RG0LE_1RB1RG_1RD1RA_0LN0RJ_1RZ0LK_0LK1LL_1RG1LM_0LL0LL_1LO1LN_0LG1LN (bbch)
BB(16)	$>f_{\omega +1}^{2}(10^{10^{57}})$
BB(18)	$>f_{\omega +2}(f_{\omega +1}^{3}(f_{\omega }^{2}(60)))$
BB(20)	$>f_{\omega +2}^{2}(21)$
BB(21)	$>f_{\omega ^{2}}^{2}(4\uparrow \uparrow 341)$
BB(40)	$>f_{\omega ^{\omega }}(75\,500)$
BB(41)	$>f_{\omega ^{\omega }}^{4}(32)$
BB(51)	$>f_{\varepsilon _{0}+1}(8)$

3 Symbols:

	Runtime	Champions
BB(2,3)	$38$	1RB2LB1RZ_2LA2RB1LB (bbch)
BB(3,3)	$\geq 119\,112\,334\,170\,342\,541>10^{17}$	0RB2LA1RA_1LA2RB1RC_1RZ1LB1LC (bbch)
BB(4,3)	$>2\uparrow \uparrow \uparrow (2^{2^{32}+1}-1)$	0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD (bbch)

4 Symbols:

	Runtime	Champions
BB(2,4)	$3\,932\,964$	1RB2LA1RA1RA_1LB1LA3RB1RZ (bbch)
BB(3,4)	$>2\uparrow ^{15}5$	1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC (bbch)

5 Symbols:

	Runtime	Champions
BB(2,5)	$>10^{10^{10^{3\,314\,360}}}$	1RB3LA4RB0RB2LA_1LB2LA3LA1RA1RZ (bbch)
BB(3,5)	$>f_{\omega }(2\uparrow ^{15}5)>f_{\omega }^{2}(15)$	1RB3LB4LC2RA4LB_2LC3RB1LC2RA1RZ_3RB1LB3LC2RC4LC (bbch)

6 Symbols:

	Runtime	Champions
BB(2,6)	$>10\uparrow \uparrow 10\uparrow \uparrow 10^{10^{115}}$	1RB3RB5RA1LB5LA2LB_2LA2RA4RB1RZ3LB2LA (bbch)

Maximum Score Function (Σ)

2 Symbols:

	Score	Champions
Σ(1)	$1$	1RZ--- (bbch)
Σ(2)	$4$	1RB1LB_1LA1RZ (bbch)
Σ(3)	$6$	1RB1RZ_0RC1RB_1LC1LA (bbch) 1RB1RC_1LC1RZ_1RA0LB (bbch) 1RB1LC_1LA1RB_1LB1RZ (bbch) 1RB1RA_1LC1RZ_1RA1LB (bbch) 1RB1LC_1RC1RZ_1LA0LB (bbch)
Σ(4)	$13$	1RB1LB_1LA0LC_1RZ1LD_1RD0RA (bbch) 1RB0RC_1LA1RA_1RZ1RD_1LD0LB (bbch)
Σ(5)	$4098$	1RB1LC_1RC1RB_1RD0LE_1LA1LD_1RZ0LA (bbch) 1RB1RA_1LC1LB_1RA1LD_1RA1LE_1RZ0LC (bbch)
Σ(6)	$>2\uparrow \uparrow 2\uparrow \uparrow 2\uparrow \uparrow 10$	1RB1RA_1RC1RZ_1LD0RF_1RA0LE_0LD1RC_1RA0RE (bbch)

3 Symbols:

	Score	Champions
Σ(2,3)	$9$	1RB2LB1RZ_2LA2RB1LB (bbch)
Σ(3,3)	$\geq 374\,676\,383$	0RB2LA1RA_1LA2RB1RC_1RZ1LB1LC (bbch)
Σ(4,3)	$>2\uparrow \uparrow \uparrow 2^{2^{32}}$	0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD (bbch)

4 Symbols:

	Score	Champions
Σ(2,4)	$2050$	1RB2LA1RA1RA_1LB1LA3RB1RZ (bbch)

5 Symbols:

	Score	Champions
Σ(2,5)	$>10^{10^{10^{3\,314\,360}}}$	1RB3LA4RB0RB2LA_1LB2LA3LA1RA1RZ (bbch)

Beeping Busy Beavers (BBB)

Beeping Busy Beaver

2 Symbols:

	Steps taken	Champions
BBB(1)	$1$
BBB(2)	$6$
BBB(3)	$55$
BBB(4)	$\geq 32\,779\,478$
BBB(5)	$\geq 10^{14006}$

3 Symbols:

	Steps taken	Champions
BBB(2,3)
BBB(3,3)	$\geq 10\uparrow \uparrow 6$

Maximum Consecutive Ones Function (Num)

2 Symbols:

	Number of Ones	Champions
num(1)	$1$	1RZ--- (bbch)
num(2)	$4$	1RB1LB_1LA1LZ (bbch)
num(3)	$6$	1RB1LC_1RC1LZ_1LA0LB (bbch)
num(4)	$12$	1RB0LA_1RC1LB_1LB1RD_1RZ0RA (bbch)
num(5)	$165$	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)	$1$	0RH (bbch) 1RH--- (bbch)
BBi(2)	$3$	0RB---_1LA--- (bbch)
BBi(3)	$5$	1RB1LB_1LA--- (bbch)
BBi(4)	$16$	1RB---_0RC---_1LC0LA (bbch)
BBi(5)	$37$	1RB2LB---_2LA2RB1LB (bbch)
BBi(6)	$123$	1RB3LA1RA0LA_2LA------3RA (bbch)
BBi(7)	$3\,932\,963$	1RB2LA1RA1RA_1LB1LA3RB--- (bbch) 1RB2LA1RA_1LC1LA2RB_---1LA--- (bbch)
BBi(8)	$>6.889\times 10^{1565}$	1RB1LA------_1RC3LB1RB---_2LA2LC---0LC (bbch)

Maximum Score (Σi)

	Score	Champions
Σi(1)	$1$	1RH--- (bbch)
Σi(2)	$2$	1RB---_1LA--- (bbch)
Σi(3)	$4$	1RB1LB_1LA--- (bbch)
Σi(4)	$5$	1RB0LB---_1LA2RA--- (bbch)
Σi(5)	$9$	1RB2LB---_2LA2RB1LB (bbch)
Σi(6)	$14$	1RB3LA1RA0LA_2LA------3RA (bbch)
Σi(7)	$2050$	1RB2LA1RA1RA_1LB1LA3RB--- (bbch) 1RB2LA1RA_1LC1LA2RB_---1LA--- (bbch)
Σi(8)	$>1.355\times 10^{783}$	1RB1LA------_1RC3LB1RB---_2LA2LC---0LC (bbch)