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A205378 Least k such that n divides s(k)-s(j) for some j where s(j)=(2j-1)^2.

%I A205378 #6 Mar 30 2012 18:58:10
%S A205378 2,2,3,2,4,3,5,2,5,4,7,3,8,5,6,3,10,5,11,4,7,7,13,3,8,8,8,5,16,6,17,5,
%T A205378 9,10,9,5,20,11,10,4,22,7,23,7,10,13,25,4,11,8,12,8,28,8,11,5,13,16,
%U A205378 31,6
%N A205378 Least k such that n divides s(k)-s(j) for some j<k, where s(j)=(2j-1)^2.
%C A205378 See A204892 for a discussion and guide to related sequences.
%t A205378 s[n_] := s[n] = (2 n - 1)^2; z1 = 600; z2 = 60;
%t A205378 Table[s[n], {n, 1, 30}]     (* A016754, odd squares *)
%t A205378 u[m_] :=  u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]]
%t A205378 Table[u[m], {m, 1, z1}]     (* A205376 *)
%t A205378 %/8                         (* A049777 *)
%t A205378 v[n_, h_] := v[n, h] = If[IntegerQ[u[h]/n], h, 0]
%t A205378 w[n_] := w[n] = Table[v[n, h], {h, 1, z1}]
%t A205378 d[n_] := d[n] = First[Delete[w[n], Position[w[n], 0]]]
%t A205378 Table[d[n], {n, 1, z2}]     (* A205377 *)
%t A205378 k[n_] := k[n] = Floor[(3 + Sqrt[8 d[n] - 1])/2]
%t A205378 m[n_] := m[n] = Floor[(-1 + Sqrt[8 n - 7])/2]
%t A205378 j[n_] := j[n] = d[n] - m[d[n]] (m[d[n]] + 1)/2
%t A205378 Table[k[n], {n, 1, z2}]     (* A205378 *)
%t A205378 Table[j[n], {n, 1, z2}]     (* A205379 *)
%t A205378 Table[s[k[n]], {n, 1, z2}]  (* A205380 *)
%t A205378 Table[s[j[n]], {n, 1, z2}]  (* A205381 *)
%t A205378 Table[s[k[n]] - s[j[n]], {n, 1, z2}]      (* A205382 *)
%t A205378 Table[(s[k[n]] - s[j[n]])/n, {n, 1, z2}]  (* A205383 *)
%Y A205378 Cf. A016754, A204892, A205383.
%K A205378 nonn
%O A205378 1,1
%A A205378 _Clark Kimberling_, Jan 26 2012