A204916 Least k such that n divides s(k)-s(j) for some j in [1,k), where s(k)=(prime(k))^2.

2, 3, 3, 3, 2, 4, 3, 3, 4, 4, 6, 4, 5, 5, 4, 3, 8, 5, 7, 4, 3, 7, 10, 4, 9, 8, 10, 5, 11, 6, 10, 5, 6, 9, 7, 5, 14, 11, 5, 4, 14, 7, 13, 7, 4, 10, 16, 5, 15, 11, 8, 8, 17, 11, 6, 5, 7, 13, 18, 6

Offset

1,1

Comments

See A204892 for a discussion and guide to related sequences

Links

Table of n, a(n) for n=1..60.

Mathematica

s[n_] := s[n] = Prime[n]^2; z1 = 1000; z2 = 60;
Table[s[n], {n, 1, 30}]  (* A001248 *)
u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]]
Table[u[m], {m, 1, z1}]             (* A204914 *)
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}]             (* A204915 *)
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}]             (* A204916 *)
Table[j[n], {n, 1, z2}]             (* A204917 *)
Table[s[k[n]], {n, 1, z2}]          (* A204918 *)
Table[s[j[n]], {n, 1, z2}]          (* A204919 *)
Table[s[k[n]] - s[j[n]], {n, 1, z2}]     (* A204920 *)
Table[(s[k[n]] - s[j[n]])/n, {n, 1, z2}] (* A204921 *)

Crossrefs

Cf. A000040, A204892, A204900, A204908.

Sequence in context: A303432 A224748 A165494 * A322225 A110049 A246577

Adjacent sequences: A204913 A204914 A204915 * A204917 A204918 A204919

Keyword

nonn

Author

Clark Kimberling, Jan 20 2012

Status

approved