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.

0, 4, 10, 20, 40, 76, 177, 387, 829, 1749, 4227, 9267, 21909

Offset

0,2

Comments

Conjecture: the last sum S for which the diameter is d, noted (d,S), are (0,3), (1,9), (2,19), (3,39), (4,86), (5,204), (6,472), (7,1180), (8,2876), (9,6880) and (10,17496). Example: (1,9) means that for S>9, d>1. - Karl Desfontaines, Dec 14 2025

Links

Table of n, a(n) for n=0..12.

Karl Desfontaines, Diameters for Sum up to 22687

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 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.
Sum S; Diameter D; Tuples T for the first diameters:
  S=4; D=1; T=(1,1,1,1).
  S=10; D=2; T=(1,2,3,4).
  S=20; D=3; T=(2,3,7,8).
  S=40; D=4; T=(3,4,14,19).
  S=76; D=5; T=(7,17,23,29).
  S=177; D=6; T=(26,47,50,54).
  S=387; D=7; T=(2,49,134,202).
  S=829; D=8; T=(1,166,267,395).
  S=1749; D=9; T=(16,70,575,1088).
  S=4227; D=10; T=(8,350,1381,2488).
  S=9267; D=11; T=(48,524,3089,5606).
  S=21909; D=12; T=(64,532,7239,14074).

Crossrefs

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

Sequence in context: A049032 A100354 A352666 * A275358 A048008 A048019

Adjacent sequences: A383583 A383584 A383585 * A383587 A383588 A383589

Keyword

nonn,more

Author

Gerold Jager, May 01 2025

Extensions

a(10)-a(12) from Karl Desfontaines, Dec 14 2025

Status

approved