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

0,2

Comments

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

Links

Table of n, a(n) for n=0..20.

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.

Example

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.

Prog

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

Crossrefs

Sequence in context: A373189 A152682 A059753 * A131665 A363610 A132158

Adjacent sequences: A255998 A255999 A256000 * A256002 A256003 A256004

Keyword

nonn,more,changed

Author

John Tromp, May 06 2015

Extensions

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

Status

approved