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 A046693 Size of smallest subset S of N={0,1,2,...,n} such that S-S=N, where S-S={abs(i-j) | i,j in S}. 7
 1, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 16, 16 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS It is easy to show that a(n+1) must be no larger than a(n)+1. Problem: Can a(n+1) ever be smaller than a(n)? Problem above solved in A103300. a(137) smaller than a(136). Except for initial term, round(sqrt(3*n + 9/4)) up to n=51. See A308766 for divergences up to n=213. See A326499 for a list of best known solutions. From Ed Pegg Jr, Jun 23 2019: (Start) Minimal marks for a sparse ruler of length n. Minimal vertices in a graceful graph with n edges. (End) LINKS Ed Pegg Jr, Table of n, a(n) for n = 0..213 Andrew Granville and Friedrich Roesler, The set of differences of a given set Andrew Granville and Friedrich Roesler, The set of differences of a given set, Amer. Math. Monthly, 106 (1999), 338-344. J. Leech, On the representation of 1, 2, ..., n by differences, J. Lond. Math. Soc. 31 (1956), 160-169. EXAMPLE a(10)=6 since all integers in {0,1,2...10} are differences of elements of {0,1,2,3,6,10}, but not of any 5-element set. a(17)=7 since all integers in {0,1,2...17} are differences of elements of {0,1,8,11,13,15,17}, but not of any 6-element set. In other words, {0,1,8,11,13,15,17} is a restricted difference basis w.r.t. A004137(7)=17. MATHEMATICA Prepend[Table[Round[Sqrt[3*n+9/4]]+If[MemberQ[A308766, n], 1, 0], {n, 1, 213}], 1] CROSSREFS Cf. A004137, A103300, A308766, A309407, A326499. - Ed Pegg Jr, Sep 14 2019 Sequence in context: A239308 A216256 A309407 * A196376 A156077 A189641 Adjacent sequences:  A046690 A046691 A046692 * A046694 A046695 A046696 KEYWORD nonn,hard AUTHOR STATUS approved

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Last modified December 12 01:57 EST 2019. Contains 329948 sequences. (Running on oeis4.)