Maximum Consecutive Ones Function - Revision history

Δ⁵: /* Champions */ used consecutive up arrows instead of up arrow exponent

2026-10-07T04:31:48Z

Champions: used consecutive up arrows instead of up arrow exponent

← Older revision		Revision as of 04:31, 7 October 2026
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	\|-		\|-
	\|[[BB(6)]]		\|[[BB(6)]]
	\|~~<math display="inline">{\geq} {\approx}10 {\uparrow}^{2} 15~~.60465~~</math>~~		\|≥ ≈ 10↑↑15.60465
	\|{{TM\|1RB0LD_1RC0RF_1LC1LA_0LE0RZ_1LF0RB_0RC0RE\|halt}}		\|{{TM\|1RB0LD_1RC0RF_1LC1LA_0LE0RZ_1LF0RB_0RC0RE\|halt}}
	\|<math>0^\infty \; \textrm{Z}\textrm{>} \; 0 \; 1^{\approx 10 {\uparrow}^{2} 15.60465} \; 0^\infty</math>		\|<math>0^\infty \; \textrm{Z}\textrm{>} \; 0 \; 1^{\approx 10 {\uparrow}^{2} 15.60465} \; 0^\infty</math>
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	\|-		\|-
	\|[[BB(4,3)]]*		\|[[BB(4,3)]]*
	\|~~<math>> 10 {\uparrow}^{4} 4</math~~>		\|> 10↑↑↑↑4
	\|{{TM\|1RB1RD1LC_2LB1RB1LC_1RZ1LA1LD_0RB2RA2RD\|halt}}		\|{{TM\|1RB1RD1LC_2LB1RB1LC_1RZ1LA1LD_0RB2RA2RD\|halt}}
	\|<math>0^\infty \; 1 \; \textrm{Z}\textrm{>} \; 1 \; (11)^{2e_4 + 8} \; 0^\infty</math>		\|<math>0^\infty \; 1 \; \textrm{Z}\textrm{>} \; 1 \; (11)^{2e_4 + 8} \; 0^\infty</math>

Loader3229: Undo revision 8965 by Loader3229 (talk)

2026-10-07T02:23:40Z

Undo revision 8965 by Loader3229 (talk)

← Older revision		Revision as of 02:23, 7 October 2026
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	\|[[BB(5)]]		\|[[BB(5)]]
	\|= 165		\|= 165
	\|{{TM\|1RB1LA_1RC1LE_1RD1RE_0LA1RC_1RZ0LB~~\|halt}} and {{TM\|0RB1LD_1LC1RB_1LD1RE_1LA1LE_1LZ0RC~~\|halt}}		\|{{TM\|1RB1LA_1RC1LE_1RD1RE_0LA1RC_1RZ0LB\|halt}}
	\|<math>0^\infty \; 1^{165} \; \textrm{Z}\textrm{>} \; 0^\infty</math>		\|<math>0^\infty \; 1^{165} \; \textrm{Z}\textrm{>} \; 0^\infty</math>
	\|[https://groups.google.com/g/busy-beaver-discuss/c/pvtXPmuMsAg/m/UP0xcmwoEAAJ Announcement] by Andrés Sancho in Feb 2025		\|[https://groups.google.com/g/busy-beaver-discuss/c/pvtXPmuMsAg/m/UP0xcmwoEAAJ Announcement] by Andrés Sancho in Feb 2025

Loader3229: /* Champions */

2026-10-07T02:19:34Z

Champions

← Older revision		Revision as of 02:19, 7 October 2026
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	\|[[BB(5)]]		\|[[BB(5)]]
	\|= 165		\|= 165
	\|{{TM\|1RB1LA_1RC1LE_1RD1RE_0LA1RC_1RZ0LB\|halt}}		\|{{TM\|1RB1LA_1RC1LE_1RD1RE_0LA1RC_1RZ0LB\|halt}} and {{TM\|0RB1LD_1LC1RB_1LD1RE_1LA1LE_1LZ0RC\|halt}}
	\|<math>0^\infty \; 1^{165} \; \textrm{Z}\textrm{>} \; 0^\infty</math>		\|<math>0^\infty \; 1^{165} \; \textrm{Z}\textrm{>} \; 0^\infty</math>
	\|[https://groups.google.com/g/busy-beaver-discuss/c/pvtXPmuMsAg/m/UP0xcmwoEAAJ Announcement] by Andrés Sancho in Feb 2025		\|[https://groups.google.com/g/busy-beaver-discuss/c/pvtXPmuMsAg/m/UP0xcmwoEAAJ Announcement] by Andrés Sancho in Feb 2025

Sligocki: /* Champions */ Note 0RZ halt trans

2026-08-09T21:42:04Z

Champions: Note 0RZ halt trans

← Older revision		Revision as of 21:42, 9 August 2026
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	<nowiki>*</nowiki> <math>e_4 = f_2(\frac{2e_3+4} 3, f_1^{2}(91))</math>, where <math>e_3 = f_2(\frac{2e_2+7} 3, f_1^{2}(91))</math>, where <math>e_2 = f_2(\frac{2e_1+7} 3, f_1^{2}(91))</math>, where <math>e_1 = 2^{95} \times 3 - 5</math>. <math>f_1(n) = 2^{n+4} \times 3 -5</math> and <math>f_2(a,b) = f_1^{2 \times f_2(a-1, b) + 11}(1)</math>, where<math>f_2(0, b) = b</math>.		<nowiki>*</nowiki> <math>e_4 = f_2(\frac{2e_3+4} 3, f_1^{2}(91))</math>, where <math>e_3 = f_2(\frac{2e_2+7} 3, f_1^{2}(91))</math>, where <math>e_2 = f_2(\frac{2e_1+7} 3, f_1^{2}(91))</math>, where <math>e_1 = 2^{95} \times 3 - 5</math>. <math>f_1(n) = 2^{n+4} \times 3 -5</math> and <math>f_2(a,b) = f_1^{2 \times f_2(a-1, b) + 11}(1)</math>, where<math>f_2(0, b) = b</math>.

	Note: All TMs here are listed in [[TNF-1RB]] format with the exception that sometimes the halt transition is chosen to be <code>1LZ</code> when that leads to a "simpler" halting configuration.		Note: All TMs here are listed in [[TNF-1RB]] format with the exception that sometimes the halt transition is chosen to be <code>0RZ</code> if that is necessary to make all final 1s consecutive or <code>1LZ</code> when that leads to a "simpler" halting configuration.

	For BB(3), there are actually 4 champion machines that all leave exactly 6 1s: {{TM\|1RB1RZ_0RC1RB_1LC1LA\|halt}}, {{TM\|1RB1LC_1LA1RB_1LB1RZ\|halt}}, {{TM\|1RB1RA_1LC1RZ_1RA1LB\|halt}}, {{TM\|1RB1LC_1RC1RZ_1LA0LB\|halt}}.		For BB(3), there are actually 4 champion machines that all leave exactly 6 1s: {{TM\|1RB1RZ_0RC1RB_1LC1LA\|halt}}, {{TM\|1RB1LC_1LA1RB_1LB1RZ\|halt}}, {{TM\|1RB1RA_1LC1RZ_1RA1LB\|halt}}, {{TM\|1RB1LC_1RC1RZ_1LA0LB\|halt}}.

Busy-beaver-oracle at 19:34, 9 August 2026

2026-08-09T19:34:20Z

← Older revision		Revision as of 19:34, 9 August 2026
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	\|<math display="inline">{\geq} {\approx}10 {\uparrow}^{2} 15.60465</math>		\|<math display="inline">{\geq} {\approx}10 {\uparrow}^{2} 15.60465</math>
	\|{{TM\|1RB0LD_1RC0RF_1LC1LA_0LE0RZ_1LF0RB_0RC0RE\|halt}}		\|{{TM\|1RB0LD_1RC0RF_1LC1LA_0LE0RZ_1LF0RB_0RC0RE\|halt}}
	\|<math>0^\infty ~~\; 1^3~~ \; \textrm{Z}\textrm{>} \; 1^{\approx 10 {\uparrow}^{2} 15.60465} \; 0^\infty</math>		\|<math>0^\infty \; \textrm{Z}\textrm{>} \; 0 \; 1^{\approx 10 {\uparrow}^{2} 15.60465} \; 0^\infty</math>
	\|		\|
	\|-		\|-

Busy-beaver-oracle at 05:26, 9 August 2026

2026-08-09T05:26:37Z

← Older revision		Revision as of 05:26, 9 August 2026
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	\|{{TM\|1RB0LD_1RC0RF_1LC1LA_0LE0RZ_1LF0RB_0RC0RE\|halt}}		\|{{TM\|1RB0LD_1RC0RF_1LC1LA_0LE0RZ_1LF0RB_0RC0RE\|halt}}
	\|<math>0^\infty \; 1^3 \; \textrm{Z}\textrm{>} \; 1^{\approx 10 {\uparrow}^{2} 15.60465} \; 0^\infty</math>		\|<math>0^\infty \; 1^3 \; \textrm{Z}\textrm{>} \; 1^{\approx 10 {\uparrow}^{2} 15.60465} \; 0^\infty</math>
	\|~~Pavel Kropitz~~		\|
	\|-		\|-
	\|[[BB(2,3)]]		\|[[BB(2,3)]]

Busy-beaver-oracle at 05:19, 9 August 2026

2026-08-09T05:19:47Z

← Older revision		Revision as of 05:19, 9 August 2026
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	\|[[BB(6)]]		\|[[BB(6)]]
	\|<math display="inline">{\geq} {\approx}10 {\uparrow}^{2} 15.60465</math>		\|<math display="inline">{\geq} {\approx}10 {\uparrow}^{2} 15.60465</math>
	\|{{TM\|~~1RB0LD_1RC0RF_1LC1LA_0LE1RZ_1LF0RB_0RC0RE~~\|halt}}		\|{{TM\|1RB0LD_1RC0RF_1LC1LA_0LE0RZ_1LF0RB_0RC0RE\|halt}}
	\|<math>0^\infty \; 1^3 \; \textrm{Z}\textrm{>} \; 1^{\approx 10 {\uparrow}^{2} 15.60465} \; 0^\infty</math>		\|<math>0^\infty \; 1^3 \; \textrm{Z}\textrm{>} \; 1^{\approx 10 {\uparrow}^{2} 15.60465} \; 0^\infty</math>
	\|Pavel Kropitz		\|Pavel Kropitz

Busy-beaver-oracle: /* Champions */ Added Pavel Kropitz's BB(6) top halter as current num(6) champion

2026-08-09T00:45:56Z

Champions: Added Pavel Kropitz's BB(6) top halter as current num(6) champion

← Older revision		Revision as of 00:45, 9 August 2026
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	\|<math>0^\infty \; 1^{165} \; \textrm{Z}\textrm{>} \; 0^\infty</math>		\|<math>0^\infty \; 1^{165} \; \textrm{Z}\textrm{>} \; 0^\infty</math>
	\|[https://groups.google.com/g/busy-beaver-discuss/c/pvtXPmuMsAg/m/UP0xcmwoEAAJ Announcement] by Andrés Sancho in Feb 2025		\|[https://groups.google.com/g/busy-beaver-discuss/c/pvtXPmuMsAg/m/UP0xcmwoEAAJ Announcement] by Andrés Sancho in Feb 2025
			\|-
			\|[[BB(6)]]
			\|<math display="inline">{\geq} {\approx}10 {\uparrow}^{2} 15.60465</math>
			\|{{TM\|1RB0LD_1RC0RF_1LC1LA_0LE1RZ_1LF0RB_0RC0RE\|halt}}
			\|<math>0^\infty \; 1^3 \; \textrm{Z}\textrm{>} \; 1^{\approx 10 {\uparrow}^{2} 15.60465} \; 0^\infty</math>
			\|Pavel Kropitz
	\|-		\|-
	\|[[BB(2,3)]]		\|[[BB(2,3)]]

Sligocki: Indicate which values are known exactly and which are bounds.

2025-12-27T16:55:29Z

Indicate which values are known exactly and which are bounds.

← Older revision		Revision as of 16:55, 27 December 2025
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	!Source		!Source
	\|-		\|-
	\| [[BB(1)]]\|\| 1 \|\| {{TM\|1RZ---\|halt}} \|\| <math>0^\infty \; 1 \; \textrm{Z}\textrm{>} \; 0^\infty</math>		\| [[BB(1)]]\|\| = 1 \|\| {{TM\|1RZ---\|halt}} \|\| <math>0^\infty \; 1 \; \textrm{Z}\textrm{>} \; 0^\infty</math>
	\|Ben-Amram, Julstrom and Zwick (1996)		\|Ben-Amram, Julstrom and Zwick (1996)
	\|-		\|-
	\|[[BB(2)]]		\|[[BB(2)]]
	\|4		\|= 4
	\|{{TM\|1RB1LB_1LA1LZ\|halt}}		\|{{TM\|1RB1LB_1LA1LZ\|halt}}
	\|<math>0^\infty \; 1 \; \textrm{<}\textrm{Z} \; 1^3 \; 0^\infty</math>		\|<math>0^\infty \; 1 \; \textrm{<}\textrm{Z} \; 1^3 \; 0^\infty</math>
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	\|-		\|-
	\|[[BB(3)]]		\|[[BB(3)]]
	\|6		\|= 6
	\|{{TM\|1RB1LC_1RC1LZ_1LA0LB\|halt}} and 3 others		\|{{TM\|1RB1LC_1RC1LZ_1LA0LB\|halt}} and 3 others
	\|<math>0^\infty \; 1 \; \textrm{<}\textrm{Z} \; 1^5 \; 0^\infty</math>		\|<math>0^\infty \; 1 \; \textrm{<}\textrm{Z} \; 1^5 \; 0^\infty</math>
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	\|-		\|-
	\|[[BB(4)]]		\|[[BB(4)]]
	\|12		\|= 12
	\|{{TM\|1RB0LA_1RC1LB_1LB1RD_1RZ0RA\|halt}}		\|{{TM\|1RB0LA_1RC1LB_1LB1RD_1RZ0RA\|halt}}
	\|<math>0^\infty \; 1^{12} \; \textrm{Z}\textrm{>} \; 0^\infty</math>		\|<math>0^\infty \; 1^{12} \; \textrm{Z}\textrm{>} \; 0^\infty</math>
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	\|-		\|-
	\|[[BB(5)]]		\|[[BB(5)]]
	\|165		\|= 165
	\|{{TM\|1RB1LA_1RC1LE_1RD1RE_0LA1RC_1RZ0LB\|halt}}		\|{{TM\|1RB1LA_1RC1LE_1RD1RE_0LA1RC_1RZ0LB\|halt}}
	\|<math>0^\infty \; 1^{165} \; \textrm{Z}\textrm{>} \; 0^\infty</math>		\|<math>0^\infty \; 1^{165} \; \textrm{Z}\textrm{>} \; 0^\infty</math>
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	\|-		\|-
	\|[[BB(2,3)]]		\|[[BB(2,3)]]
	\|6		\|= 6
	\|{{TM\|1RB1LA1LB_0LA2RA1RZ\|halt}}		\|{{TM\|1RB1LA1LB_0LA2RA1RZ\|halt}}
	\|<math>0^\infty \; 1^2 \; \textrm{Z}\textrm{>} \; 1^{4} \; 0^\infty</math>		\|<math>0^\infty \; 1^2 \; \textrm{Z}\textrm{>} \; 1^{4} \; 0^\infty</math>
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	\|-		\|-
	\|[[BB(3,3)]]		\|[[BB(3,3)]]
	\|12		\|≥ 12
	\|{{TM\|1RB1RA1RZ_1LC1LC2LA_2RA1LB1LA\|halt}}		\|{{TM\|1RB1RA1RZ_1LC1LC2LA_2RA1LB1LA\|halt}}
	\|<math>0^\infty \; 1^2 \; \textrm{Z}\textrm{>} \; 1^{10} \; 0^\infty</math>		\|<math>0^\infty \; 1^2 \; \textrm{Z}\textrm{>} \; 1^{10} \; 0^\infty</math>

Polygon: /* Champions */ added num(2,3)

2025-12-27T12:37:03Z

Champions: added num(2,3)

← Older revision		Revision as of 12:37, 27 December 2025
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	\|<math>0^\infty \; 1^{165} \; \textrm{Z}\textrm{>} \; 0^\infty</math>		\|<math>0^\infty \; 1^{165} \; \textrm{Z}\textrm{>} \; 0^\infty</math>
	\|[https://groups.google.com/g/busy-beaver-discuss/c/pvtXPmuMsAg/m/UP0xcmwoEAAJ Announcement] by Andrés Sancho in Feb 2025		\|[https://groups.google.com/g/busy-beaver-discuss/c/pvtXPmuMsAg/m/UP0xcmwoEAAJ Announcement] by Andrés Sancho in Feb 2025
			\|-
			\|[[BB(2,3)]]
			\|6
			\|{{TM\|1RB1LA1LB_0LA2RA1RZ\|halt}}
			\|<math>0^\infty \; 1^2 \; \textrm{Z}\textrm{>} \; 1^{4} \; 0^\infty</math>
			\|
	\|-		\|-
	\|[[BB(3,3)]]		\|[[BB(3,3)]]