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 A364153 a(n) is the smallest positive integer such that from the set {1, 2, ..., a(n)} one can choose a sequence (s(1), s(2), ..., s(n)) in which every segment has a unique sum. 1
 1, 2, 3, 5, 6, 7, 9, 10, 12, 13, 14, 17, 18 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A segment is a subsequence of consecutive elements. Conjecture: There exists C such that a(n) < C*n for every sufficiently large n. LINKS Table of n, a(n) for n=1..13. EXAMPLE a(6) = 7, because there exists a 6-element sequence on the set {1,2,...,7} with unique segment sums: (2,1,7,6,5,4) and 7 is the least positive integer with such property. The sums in the segments are: 2, 1, 7, 6, 5, 4 for 1-element segments; 3, 8, 13, 11, 9 for 2-element segments; 10, 14, 18, 15 for 3-element segments; 16, 19, 22 for 4-element segments; 21, 23 for 5-element segments; and 25 for the full set. a(13) = 18 and the exemplary corresponding 13-element sequence is (1, 6, 15, 8, 11, 9, 16, 17, 18, 13, 14, 10, 2). PROG (PARI) a(n, m=n+6) = my(k=1, s=vector(n, i, []), t, u=m, v=vector(n)); while(k, t=0; v[k]++; if(k==n, if(v[n]

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Last modified August 12 15:11 EDT 2024. Contains 375113 sequences. (Running on oeis4.)