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A205442 Least k such that n divides s(k)-s(j) for some j where s(j) is the (2j-1)-st Fibonacci number.

%I A205442 #5 Mar 30 2012 18:58:11
%S A205442 2,3,3,3,6,4,5,4,7,7,4,4,8,6,11,5,10,7,6,7,5,6,13,7,26,9,19,6,5,12,9,
%T A205442 5,5,10,21,7,20,6,15,16,11,6,23,6,31,13,9,7,29,27,19,9,28,19,6,13,7,7,
%U A205442 16,12
%N A205442 Least k such that n divides s(k)-s(j) for some j<k, where s(j) is the (2j-1)-st Fibonacci number.
%C A205442 See A204892 for a discussion and guide to related sequences.
%t A205442 s[n_] := s[n] = Fibonacci[2*n - 1]; z1 = 500; z2 = 60;
%t A205442 Table[s[n], {n, 1, 30}]         (* A001519 *)
%t A205442 u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]]
%t A205442 Table[u[m], {m, 1, z1}]         (* A205371 *)
%t A205442 v[n_, h_] := v[n, h] = If[IntegerQ[u[h]/n], h, 0]
%t A205442 w[n_] := w[n] = Table[v[n, h], {h, 1, z1}]
%t A205442 d[n_] := d[n] = First[Delete[w[n], Position[w[n], 0]]]
%t A205442 Table[d[n], {n, 1, z2}]         (* A205441 *)
%t A205442 k[n_] := k[n] = Floor[(3 + Sqrt[8 d[n] - 1])/2]
%t A205442 m[n_] := m[n] = Floor[(-1 + Sqrt[8 n - 7])/2]
%t A205442 j[n_] := j[n] = d[n] - m[d[n]] (m[d[n]] + 1)/2
%t A205442 Table[k[n], {n, 1, z2}]         (* A205442 *)
%t A205442 Table[j[n], {n, 1, z2}]         (* A205443 *)
%t A205442 Table[s[k[n]], {n, 1, z2}]      (* A205444 *)
%t A205442 Table[s[j[n]], {n, 1, z2}]      (* A205445 *)
%t A205442 Table[s[k[n]] - s[j[n]], {n, 1, z2}]      (* A205446 *)
%t A205442 Table[(s[k[n]] - s[j[n]])/n, {n, 1, z2}]  (* A205447 *)
%Y A205442 Cf. A001519, A205447, A204892.
%K A205442 nonn
%O A205442 1,1
%A A205442 _Clark Kimberling_, Jan 27 2012