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.

0, 5, 15, 31, 71, 176, 444, 1287, 3600

Offset

0,2

Links

Table of n, a(n) for n=0..8.

Karl Desfontaines, Diameters for all sum from 0 to 3979 with examples

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.

Example

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)
From Karl Desfontaines, Dec 10 2025: (Start)
  a(7) = 1287 due to (5,41,177,417,647),
  a(8) = 3600 due to (14,31,509,1185,1861). (End)

Crossrefs

Cf. A256001 (for 3-tuples), A383586 (for 4-tuples), A383588 (for 6-tuples).

Sequence in context: A037984 A298032 A073361 * A155013 A134887 A228599

Adjacent sequences: A383584 A383585 A383586 * A383588 A383589 A383590

Keyword

nonn,more

Author

Gerold Jager, May 01 2025

Extensions

a(6) from Bert Dobbelaere, May 11 2025

a(7)-a(8) from Karl Desfontaines, Dec 10 2025

Status

approved