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 A205018 Least k such that n divides s(k)-s(j) for some j satisfying 1<=j
 2, 2, 3, 2, 3, 3, 4, 4, 4, 3, 6, 5, 7, 4, 6, 8, 9, 4, 10, 6, 8, 6, 12, 5, 7, 7, 7, 5, 15, 6, 16, 16, 8, 9, 8, 6, 19, 10, 9, 6, 21, 8, 22, 7, 10, 12, 24, 9, 10, 7, 11, 8, 27, 7, 13, 11, 12, 15, 30, 8 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS See A204892 for a discussion and guide to related sequences. LINKS MATHEMATICA s[n_] := s[n] = n*(n + 1); z1 = 500; z2 = 60; Table[s[n], {n, 1, 30}]   (* A002378 *) u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]] Table[u[m], {m, 1, z1}]   (* A205016 *) 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}]   (* A205017 *) 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}]      (* A205018 *) Table[j[n], {n, 1, z2}]      (* A205028 *) Table[s[k[n]], {n, 1, z2}]   (* A205029 *) Table[s[j[n]], {n, 1, z2}]   (* A205030 *) Table[s[k[n]] - s[j[n]], {n, 1, z2}]      (* A205031 *) Table[(s[k[n]] - s[j[n]])/n, {n, 1, z2}]  (* A205032 *) CROSSREFS Cf. A002378, A204892, A205016. Sequence in context: A303297 A107452 A349198 * A286716 A029213 A029209 Adjacent sequences:  A205015 A205016 A205017 * A205019 A205020 A205021 KEYWORD nonn AUTHOR Clark Kimberling, Jan 22 2012 STATUS approved

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Last modified December 4 02:40 EST 2021. Contains 349469 sequences. (Running on oeis4.)