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, 1044

Offset

0,2

Links

Table of n, a(n) for n=0..6.

Karl Desfontaines, All Diameters from S=0 to S=1439 with additional info

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 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)
a(6) = 1044 due to (11,73,83,265,278,334). - Karl Desfontaines, Dec 23 2025

Crossrefs

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

Sequence in context: A175729 A081266 A087863 * A212656 A051941 A212707

Adjacent sequences: A383585 A383586 A383587 * A383589 A383590 A383591

Keyword

nonn,more

Author

Gerold Jager, May 01 2025

Extensions

a(5) from Bert Dobbelaere, May 11 2025

a(6) from Karl Desfontaines, Dec 23 2025

Status

approved