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A205394 Least k such that n divides s(k)-s(j) for some j where s(j)=ceiling(j^2/2).

%I A205394 #5 Mar 30 2012 18:58:11
%S A205394 2,3,3,3,5,4,4,5,8,6,5,5,6,8,8,6,6,9,8,7,10,12,7,7,10,14,8,9,11,8,8,
%T A205394 10,9,18,12,9,10,20,9,9,15,10,11,13,10,24,12,10,10,15,20,15,11,12,16,
%U A205394 11,14,30,11,11,22,32,15,12,18,14,12,19,26,12,12,13,14,38,20,21
%N A205394 Least k such that n divides s(k)-s(j) for some j<k, where s(j)=ceiling(j^2/2).
%C A205394 See A204892 for a discussion and guide to related sequences.
%t A205394 s[n_] := s[n] = Floor[(n^2 + 1)/2]; z1 = 800; z2 = 80;
%t A205394 Table[s[n], {n, 1, 30}]     (* A000982 *)
%t A205394 u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]]
%t A205394 Table[u[m], {m, 1, z1}]     (* A205392 *)
%t A205394 v[n_, h_] := v[n, h] = If[IntegerQ[u[h]/n], h, 0]
%t A205394 w[n_] := w[n] = Table[v[n, h], {h, 1, z1}]
%t A205394 d[n_] := d[n] = First[Delete[w[n], Position[w[n], 0]]]
%t A205394 Table[d[n], {n, 1, z2}]     (* A205393 *)
%t A205394 k[n_] := k[n] = Floor[(3 + Sqrt[8 d[n] - 1])/2]
%t A205394 m[n_] := m[n] = Floor[(-1 + Sqrt[8 n - 7])/2]
%t A205394 j[n_] := j[n] = d[n] - m[d[n]] (m[d[n]] + 1)/2
%t A205394 Table[k[n], {n, 1, z2}]         (* A205394 *)
%t A205394 Table[j[n], {n, 1, z2}]         (* A205395 *)
%t A205394 Table[s[k[n]], {n, 1, z2}]      (* A205396 *)
%t A205394 Table[s[j[n]], {n, 1, z2}]      (* A205397 *)
%t A205394 Table[s[k[n]] - s[j[n]], {n, 1, z2}]      (* A205398 *)
%t A205394 Table[(s[k[n]] - s[j[n]])/n, {n, 1, z2}]  (* A205399 *)
%Y A205394 Cf. A000982, A204892, A205399.
%K A205394 nonn
%O A205394 1,1
%A A205394 _Clark Kimberling_, Jan 27 2012