A205450 Least k such that n divides s(k) - s(j) for some j

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, 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, 8, 30, 32

Offset: 1

Author

Clark Kimberling, Jan 27 2012

Keywords

• nonn

Comments

See A204892 for a discussion and guide to related sequences.

Crossrefs

Cf. A001906, A205455, A204892.

Programs

Mathematica

s[n_] := s[n] = Fibonacci[2*n]; z1 = 500; z2 = 60;
Table[s[n], {n, 1, 30}]     (* A001906 *)
u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]]
Table[u[m], {m, 1, z1}]     (* A205448 *)
v[n_, h_] := v[n, h] = If[IntegerQ[u[h]/n], h, 0]
w[n_] := w[n] = Table[v[n, h], {h, 1, z1}]
d[n_] := d[n] = First[Delete[w[n], Position[w[n], 0]]]
Table[d[n], {n, 1, z2}]     (* A205449 *)
k[n_] := k[n] = Floor[(3 + Sqrt[8 d[n] - 1])/2]
m[n_] := m[n] = Floor[(-1 + Sqrt[8 n - 7])/2]
j[n_] := j[n] = d[n] - m[d[n]] (m[d[n]] + 1)/2
Table[k[n], {n, 1, z2}]         (* A205450 *)
Table[j[n], {n, 1, z2}]         (* A205451 *)
Table[s[k[n]], {n, 1, z2}]      (* A205452 *)
Table[s[j[n]], {n, 1, z2}]      (* A205453 *)
Table[s[k[n]] - s[j[n]], {n, 1, z2}]      (* A205454 *)
Table[(s[k[n]] - s[j[n]])/n, {n, 1, z2}]  (* A205455 *)