A205146
Least k such that n divides s(k)-s(j) for some j satisfying 1<=j
2, 3, 2, 3, 3, 4, 4, 5, 2, 3, 5, 5, 6, 4, 7, 5, 7, 5, 8, 3, 4, 5, 9, 6, 12, 6, 5, 7, 3, 7, 4, 5, 5, 7, 15, 5, 12, 8, 6, 8, 7, 4, 6, 7, 7, 9, 10, 6, 8, 12, 7, 10, 16, 5, 16, 13, 8, 10, 9, 7, 16, 4, 10, 5, 14, 5, 8, 10, 20, 16, 4, 6, 18, 12, 14, 13, 7, 6, 9, 11
Offset: 1
Keywords
Links
- Michel Marcus, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
s[n_] := s[n] = Prime[n] Prime[n + 1]; z1 = 400; z2 = 60; Table[s[n], {n, 1, 30}] (* A006094 *) u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]] Table[u[m], {m, 1, z1}] (* A205144 *) 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}] (* A205145 *) 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}] (* A205146 *) Table[j[n], {n, 1, z2}] (* A205147 *) Table[s[k[n]], {n, 1, z2}] (* A205148 *) Table[s[j[n]], {n, 1, z2}] (* A205149 *) Table[s[k[n]] - s[j[n]], {n, 1, z2}] (* A205150 *) Table[(s[k[n]] - s[j[n]])/n, {n, 1, z2}] (* A205151 *) -
PARI
s(m) = prime(m)*prime(m+1); isok(k, n) = my(sk=s(k)); for (j=1, k-1, if (!Mod(sk-s(j), n), return (k))); a(n) = my(k=1); while (!isok(k, n), k++); k; \\ Michel Marcus, Jul 23 2021
Extensions
More terms from Michel Marcus, Jul 23 2021
Comments