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 A204900 Least k such that n divides s(k)-s(j) for some j in [1,k), where s(k) is the k-th odd prime. 23
 2, 2, 4, 3, 5, 4, 6, 4, 8, 5, 9, 6, 9, 6, 11, 7, 11, 8, 12, 8, 14, 9, 15, 9, 15, 9, 16, 10, 17, 11, 18, 11, 19, 11, 20, 12, 21, 12, 22, 13, 23, 14, 23, 14, 24, 15, 24, 15, 25, 15, 27, 16, 28, 16, 29, 16, 30, 17, 31, 18, 30, 18, 31, 18, 32, 19, 32, 19, 34, 20, 34, 21, 34 (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] = Prime[n + 1]; z1 = 400; z2 = 50; Table[s[n], {n, 1, 30}]      (* A065091 *) u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]] Table[u[m], {m, 1, z1}]      (* A204898 *) 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}]      (* A204899 *) 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}]      (* A204900 *) Table[j[n], {n, 1, z2}]      (* A204901 *) Table[s[k[n]], {n, 1, z2}]   (* A204902 *) Table[s[j[n]], {n, 1, z2}]   (* A204903 *) Table[s[k[n]] - s[j[n]], {n, 1, z2}]     (* A204904 *) Table[(s[k[n]] - s[j[n]])/n, {n, 1, z2}] (* A000034 conjectured *) CROSSREFS Cf. A000040, A065091, A204892. Sequence in context: A215675 A132802 A268353 * A070803 A071693 A225381 Adjacent sequences:  A204897 A204898 A204899 * A204901 A204902 A204903 KEYWORD nonn,changed AUTHOR Clark Kimberling, Jan 20 2012 STATUS approved

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