%I #5 Mar 30 2012 18:58:11

%S 2,2,4,4,3,4,3,6,4,4,6,8,4,7,12,9,5,4,10,4,8,7,7,8,13,5,5,9,8,14,16,

%T 15,12,5,11,12,10,10,16,9,6,8,12,16,14,7,5,12,10,14,20,5,14,5,10,9,20,

%U 8,30,32

%N Least k such that n divides s(k)-s(j) for some j<k, where s(j) is the 2j-th Fibonacci number.

%C See A204892 for a discussion and guide to related sequences.

%t Least k such that n divides s(k)-s(j) for some j<k, where s(j) is the 2j-th Fibonacci number.

%t See A204892 for a discussion and guide to related sequences.

%t s[n_] := s[n] = Fibonacci[2*n]; z1 = 500; z2 = 60;

%t Table[s[n], {n, 1, 30}] (* A001906 *)

%t u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]]

%t Table[u[m], {m, 1, z1}] (* A205448 *)

%t v[n_, h_] := v[n, h] = If[IntegerQ[u[h]/n], h, 0]

%t w[n_] := w[n] = Table[v[n, h], {h, 1, z1}]

%t d[n_] := d[n] = First[Delete[w[n], Position[w[n], 0]]]

%t Table[d[n], {n, 1, z2}] (* A205449 *)

%t k[n_] := k[n] = Floor[(3 + Sqrt[8 d[n] - 1])/2]

%t m[n_] := m[n] = Floor[(-1 + Sqrt[8 n - 7])/2]

%t j[n_] := j[n] = d[n] - m[d[n]] (m[d[n]] + 1)/2

%t Table[k[n], {n, 1, z2}] (* A205450 *)

%t Table[j[n], {n, 1, z2}] (* A205451 *)

%t Table[s[k[n]], {n, 1, z2}] (* A205452 *)

%t Table[s[j[n]], {n, 1, z2}] (* A205453 *)

%t Table[s[k[n]] - s[j[n]], {n, 1, z2}] (* A205454 *)

%t Table[(s[k[n]] - s[j[n]])/n, {n, 1, z2}] (* A205455 *)

%Y Cf. A001906, A205455, A204892.

%K nonn

%O 1,1

%A _Clark Kimberling_, Jan 27 2012