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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.

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

A383587 a(n) is the minimum sum of a nonnegative integer 5-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, 5, 15, 31, 71, 176, 444

Offset: 0

Gerold Jager, May 01 2025

			The 5-tuple (1,2,3,4,5), with sum 1+2+3+4+5=15, takes two moves to reach a 0 component. (1,2,3,4,5) -> (2,2,2,4,5) -> (0,4,2,4,5) and is a minimum sum for n=2.
From _Bert Dobbelaere_, May 11 2025: (Start)
  a(3) = 31 due to (1,4,6,9,11)
  a(4) = 71 due to (1,8,13,19,30)
  a(5) = 176 due to (7,11,23,61,74)
  a(6) = 444 due to (7,20,123,139,155)
(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), A383588 (for 6-tuples).

a(6) from Bert Dobbelaere, May 11 2025

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)

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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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A383587 a(n) is the minimum sum of a nonnegative integer 5-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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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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