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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.

%I A383587 #17 May 12 2025 19:42:39
%S A383587 0,5,15,31,71,176,444
%N 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.
%H A383587 Gerold Jäger and Tuomo Lehtilä, <a href="https://arxiv.org/abs/2504.03039">The Generalized Double Pouring Problem: Analysis, Bounds and Algorithms</a>, arXiv:2504.03039 [math.CO], 2025. See Definition 4(a) p. 3, and Table 1, p. 12.
%e A383587 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.
%e A383587 From _Bert Dobbelaere_, May 11 2025: (Start)
%e A383587   a(3) = 31 due to (1,4,6,9,11)
%e A383587   a(4) = 71 due to (1,8,13,19,30)
%e A383587   a(5) = 176 due to (7,11,23,61,74)
%e A383587   a(6) = 444 due to (7,20,123,139,155)
%e A383587 (End)
%Y A383587 Cf. A256001 (for 3-tuples), A383586 (for 4-tuples), A383588 (for 6-tuples).
%K A383587 nonn,more
%O A383587 0,2
%A A383587 _Gerold Jager_, May 01 2025
%E A383587 a(6) from _Bert Dobbelaere_, May 11 2025