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 A205010 Least k such that n divides s(k)-s(j) for some j satisfying 1<=j
 2, 3, 4, 3, 3, 4, 4, 5, 4, 5, 8, 7, 6, 4, 8, 5, 5, 4, 4, 8, 7, 8, 5, 7, 5, 6, 7, 7, 6, 8, 12, 5, 8, 5, 8, 10, 10, 8, 9, 9, 6, 7, 16, 8, 10, 11, 8, 7, 8, 5, 7, 10, 8, 7, 10, 7, 8, 6, 20, 8 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS See A204892 for a discussion and guide to related sequences. LINKS Table of n, a(n) for n=1..60. MATHEMATICA s[n_] := s[n] = Binomial[2 (n - 1), n - 1]; z1 = 700; z2 = 60; Table[s[n], {n, 1, 30}] (* A000984 *) u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]] Table[u[m], {m, 1, z1}] (* A205008 *) v[n_, h_] := v[n, h] = If[IntegerQ[u[h]/n], h, 0] w[n_] := w[n] = Table[v[n, h], {h, 1, z1}] d[n_] := d[n] = First[Delete[w[n], Position[w[n], 0]]] Table[d[n], {n, 1, z2}] (* A205009 *) k[n_] := k[n] = Floor[(3 + Sqrt[8 d[n] - 1])/2] m[n_] := m[n] = Floor[(-1 + Sqrt[8 n - 7])/2] j[n_] := j[n] = d[n] - m[d[n]] (m[d[n]] + 1)/2 Table[k[n], {n, 1, z2}] (* A205010 *) Table[j[n], {n, 1, z2}] (* A205011 *) Table[s[k[n]], {n, 1, z2}] (* A205012 *) Table[s[j[n]], {n, 1, z2}] (* A205013 *) Table[s[k[n]] - s[j[n]], {n, 1, z2}] (* A205014 *) Table[(s[k[n]] - s[j[n]])/n, {n, 1, z2}] (* A205015 *) CROSSREFS Cf. A000984, A204892, A205008. Sequence in context: A322808 A352899 A119352 * A204932 A079086 A017839 Adjacent sequences: A205007 A205008 A205009 * A205011 A205012 A205013 KEYWORD nonn AUTHOR Clark Kimberling, Jan 22 2012 STATUS approved

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Last modified May 26 04:31 EDT 2024. Contains 372807 sequences. (Running on oeis4.)