A383587 -id:A383587 - cp's OEIS frontend

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

John Tromp, May 06 2015

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

			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.

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.

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

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

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

A383586 a(n) is the minimum sum of a nonnegative integer 4-tuple 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.

Original entry on oeis.org

0, 4, 10, 20, 40, 76, 177, 387, 829, 1749

Offset: 0

Gerold Jager, May 01 2025

			The 4-tuple (1,2,3,4), with sum 1+2+3+4=10, takes two moves to reach a 0 component. (1,2,3,4) -> (2,2,2,4) -> (0,4,2,4) and is a minimum sum for n=2.

Gerold Jäger and Tuomo Lehtilä, The Generalized Double Pouring Problem: Analysis, Bounds and Algorithms, arXiv:2504.03039 [math.CO], 2025. See Definition 4(a) p. 3, and Table 1, p. 12.

Cf. A256001 (for 3-tuples), A383587 (for 5-tuples), A383588 (for 6-tuples)

A383588 a(n) is the minimum sum of a nonnegative integer 6-tuple 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.

Original entry on oeis.org

0, 6, 21, 45, 123, 335

Offset: 0

Gerold Jager, May 01 2025

			The 6-tuple (1,2,3,4,5,6), with sum 1+2+3+4+5+6=21, takes two moves to reach a 0 component. (1,2,3,4,5,6) -> (2,2,2,4,5,6) -> (0,4,2,4,5,6) and is a minimum sum for n=2.
From _Bert Dobbelaere_, May 11 2025: (Start)
  a(3) = 45 due to (1,4,6,9,11,14)
  a(4) = 123 due to (1,9,13,20,37,43)
  a(5) = 335 due to (7,23,40,45,81,139)
(End)

Gerold Jäger and Tuomo Lehtilä, The Generalized Double Pouring Problem: Analysis, Bounds and Algorithms, arXiv:2504.03039 [math.CO], 2025. See Definition 4(a) p. 3, and Table 1, p. 12.

Cf. A256001 (for 3-tuples), A383586 (for 4-tuples), A383587 (for 5-tuples).

a(5) from Bert Dobbelaere, May 11 2025

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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.

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A383586 a(n) is the minimum sum of a nonnegative integer 4-tuple 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.

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A383588 a(n) is the minimum sum of a nonnegative integer 6-tuple 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.

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