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8 states Ackermann level [[probviously]] halting cryptids. --Jacobzheng (talk) 05:46, 16 November 2024 (UTC) | |||
== Three-Way Deal (14 states, 8 symbols) == | |||
Let <math>M(n)=(3n)!/(n!)^3</math> count the deals of <math>3n</math> distinct cards into three labelled hands of size <math>n</math>. The conjecture is that exactly 59 positive integers <math>n</math> satisfy <math>\gcd(M(n),35)=1</math>. These are the positive integers whose base-5 digits are at most 1 and whose base-7 digits are at most 2. | |||
The machine halts from a blank tape on finding a 60th such integer. An exhaustive search below <math>5^{50000}</math> found 59. Is this conjecture or an equivalent machine already known? [[Media:Three-Way Deal verification.zip|Transition table, proof of the halting criterion, and verification scripts]]. [[User:Shivamshaiv|Shivamshaiv]] ([[User talk:Shivamshaiv|talk]]) 08:41, 26 October 2026 (UTC) | |||
Latest revision as of 08:41, 26 October 2026
1LG1RH_0LD1RC_0LD0LG_0RE1LD_0RF1RA_1RB1RF_1LC1LG_---0RF (bbch)
1RG1RH_0LD1RC_0LD0LG_0RE1LD_0RF1RA_1RB1RF_1LC1LG_---0RF (bbch)
1LC1LA_0LD1RC_0LD0LA_0RE1LD_0RG1RF_---1RH_1RB1RG_0RA0RG (bbch)
8 states Ackermann level probviously halting cryptids. --Jacobzheng (talk) 05:46, 16 November 2024 (UTC)
Three-Way Deal (14 states, 8 symbols)
Let count the deals of distinct cards into three labelled hands of size . The conjecture is that exactly 59 positive integers satisfy . These are the positive integers whose base-5 digits are at most 1 and whose base-7 digits are at most 2.
The machine halts from a blank tape on finding a 60th such integer. An exhaustive search below found 59. Is this conjecture or an equivalent machine already known? Transition table, proof of the halting criterion, and verification scripts. Shivamshaiv (talk) 08:41, 26 October 2026 (UTC)