A381812 Number of moves required to reach a position with the maximum number of heads in the game of blet with 2*n coins.

1, 1, 2, 5, 3, 6, 11, 7, 10, 17, 11, 16, 25, 15, 22, 33, 21, 28, 41, 27, 34

Offset: 2

Author

Pontus von Brömssen, Mar 08 2025

Keywords

• nonn
• more

Comments

See A075273 or Rodriguez Villegas, Sadun, and Voloch (2002) for the definition of blet.

Rodriguez Villegas, Sadun, and Voloch (2002) prove that the maximum number of heads achievable is A047206(n).

Examples

			For n = 5, a(5) = 5 moves are needed to go from HTHTHTHTHT to a sequence with the maximum number A047206(5) = 8 of heads: HTHTHTHTHT -> THHTHTHTHH -> THHTHTTHTH -> THHHTHTHTH -> THHHHTHHTH -> HHHHHTHHHT.
		

Links

• Michael S. Branicky, Python program for OEIS A381812
• Fernando Rodriguez Villegas, Lorenzo Sadun, and José Felipe Voloch, Blet: a mathematical puzzle, The American Mathematical Monthly 109 (2002), Issue 8, 729-740.

Crossrefs

Cf. A047206, A075273, A381813, A381814.

Programs

Python

# see linked program

Extensions

a(17)-a(18) from Michael S. Branicky, Mar 11 2025

a(19)-a(22) from Bert Dobbelaere, Mar 15 2025