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

%I A204916 #5 Mar 30 2012 18:58:08
%S A204916 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,
%T A204916 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
%N A204916 Least k such that n divides s(k)-s(j) for some j in [1,k), where s(k)=(prime(k))^2.
%C A204916 See A204892 for a discussion and guide to related sequences
%t A204916 s[n_] := s[n] = Prime[n]^2; z1 = 1000; z2 = 60;
%t A204916 Table[s[n], {n, 1, 30}]  (* A001248 *)
%t A204916 u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]]
%t A204916 Table[u[m], {m, 1, z1}]             (* A204914 *)
%t A204916 v[n_, h_] := v[n, h] = If[IntegerQ[u[h]/n], h, 0]
%t A204916 w[n_] := w[n] = Table[v[n, h], {h, 1, z1}]
%t A204916 d[n_] := d[n] = First[Delete[w[n], Position[w[n], 0]]]
%t A204916 Table[d[n], {n, 1, z2}]             (* A204915 *)
%t A204916 k[n_] := k[n] = Floor[(3 + Sqrt[8 d[n] - 1])/2]
%t A204916 m[n_] := m[n] = Floor[(-1 + Sqrt[8 n - 7])/2]
%t A204916 j[n_] := j[n] = d[n] - m[d[n]] (m[d[n]] + 1)/2
%t A204916 Table[k[n], {n, 1, z2}]             (* A204916 *)
%t A204916 Table[j[n], {n, 1, z2}]             (* A204917 *)
%t A204916 Table[s[k[n]], {n, 1, z2}]          (* A204918 *)
%t A204916 Table[s[j[n]], {n, 1, z2}]          (* A204919 *)
%t A204916 Table[s[k[n]] - s[j[n]], {n, 1, z2}]     (* A204920 *)
%t A204916 Table[(s[k[n]] - s[j[n]])/n, {n, 1, z2}] (* A204921 *)
%Y A204916 Cf. A000040, A204892, A204900, A204908.
%K A204916 nonn
%O A204916 1,1
%A A204916 _Clark Kimberling_, Jan 20 2012