A364132 a(n) is the smallest positive integer such that from the set {1, 2, ..., a(n)} one can choose an increasing sequence (s(1), s(2), ..., s(n)) in which every segment has a unique sum of elements.
1, 2, 4, 5, 7, 10, 12, 13, 15, 18, 21, 24, 25, 29, 30, 33, 36, 38, 41, 47, 50, 52
Offset: 1
Examples
a(6) = 10, because there exists a 6-element increasing sequence on {1,2,...,10} with unique segment sums, namely (1,2,4,5,8,10) and 10 is the least positive integer with that property. The sums in the segments are: 1, 2, 4, 5, 8, 10 for 1-element segments; 3, 6, 9, 13, 18 for 2-element segments; 7, 11, 17, 23 for 3-element segments; 12, 19, 27 for 4-element segments; 20, 29 for 5-element segments; and 30 for the full set.
a(13) = 25 and the corresponding 13-element subsequence is (1,2,11,15,16,17,18,19,20,21,22,24,25).
Programs
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PARI
a(n, m=2*n) = my(k=1, s=vector(n, i, []), t, u=m, v=vector(n)); while(k>1||v[1]
Extensions
a(14)-a(22) from Jinyuan Wang, Jul 10 2023
Comments