A256001 Minimum sum of a nonnegative integer triple that takes n moves to reach a 0 component, where a move picks two components, subtracts the smaller from the larger, and doubles the smaller.

0, 3, 6, 11, 15, 23, 27, 45, 81, 105, 195, 329, 597, 885, 1425, 2793, 4725, 8025, 14265, 23205, 41685

Offset: 0

Author

John Tromp, May 06 2015

Keywords

• nonn
• more

Comments

a(21) > 65532. - Karl Desfontaines, Mar 02 2022

Examples

			The triple (1,2,3) is the triple with minimum sum that has no 0's or equal members and reaches a 0 after the 2 moves (1,2,3) -> (2,2,2) -> (4,0,2). Since the sum of this triple is 6, a(2) = 6.
		

Links

• IBM's Ponder This, 3 people betting game, May 2015, challenge essentially asks for (a witness for) a(12).
• Fabian Frei, Peter Rossmanith, and David Wehner, An Open Pouring Problem, 10th International Conference on Fun with Algorithms (FUN 2021). Schloss Dagstuhl-Leibniz-Zentrum für Informatik, 14:1-9.
• John Tromp, C program computing diameter and witness for each sum.

Crossrefs

Cf. A383586 (for 4-tuples), A383587 (for 5-tuples), A383588 (for 6-tuples).

Programs

C

// See link above for a C program from whose output the terms above were derived.

Extensions

a(19)-a(20) from Karl Desfontaines, Mar 02 2022