A205153
Least k such that n divides s(k)-s(j) for some j
2, 2, 3, 4, 3, 4, 6, 4, 5, 8, 5, 6, 9, 6, 7, 10, 7, 9, 10, 8, 9, 8, 14, 9, 10, 9, 11, 10, 14, 10, 20, 14, 11, 16, 11, 12, 20, 12, 13, 22, 13, 16, 17, 14, 16, 14, 15, 16, 17, 15, 16, 15, 30, 16, 17, 16, 18, 17, 23, 17, 20, 31, 18, 20, 18, 19, 20, 19, 21, 20, 22, 20, 24
Offset: 1
Keywords
Programs
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Mathematica
s[n_] := s[n] = (Prime[n + 1] + Prime[n + 2])/2; z1 = 1100; z2 = 80; Table[s[n], {n, 1, 30}] (* A024675 *) u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]] Table[u[m], {m, 1, z1}] (* A204980 *) 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}] (* A205152 *) 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}] (* A205153 *) Table[j[n], {n, 1, z2}] (* A205154 *) Table[s[k[n]], {n, 1, z2}] (* A205372 *) Table[s[j[n]], {n, 1, z2}] (* A205373 *) Table[s[k[n]] - s[j[n]], {n, 1, z2}] (* A205374 *) Table[(s[k[n]] - s[j[n]])/n, {n, 1, z2}] (* A205375 *)
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