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.

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

Offset: 1

Author

Clark Kimberling, Jan 20 2012

Keywords

• nonn

Comments

See A204892 for a discussion and guide to related sequences

Crossrefs

Cf. A000040, A065091, A204892.

Programs

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 *)