A205114 Least k such that n divides L(k)-L(j) for some j satisfying 1<=jA000032).

2, 2, 3, 4, 5, 4, 5, 5, 7, 5, 6, 8, 7, 6, 6, 10, 6, 7, 10, 8, 10, 7, 8, 9, 7, 7, 16, 7, 8, 10, 16, 11, 11, 11, 10, 8, 13, 10, 11, 8, 11, 14, 8, 8, 12, 8, 9, 11, 11, 16, 13, 13, 12, 16, 12, 10, 17, 9, 14, 10

Offset: 1

Author

Clark Kimberling, Jan 22 2012

Keywords

• nonn

Comments

See A204892 for a discussion and guide to related sequences.

Crossrefs

Cf. A000032, A204892, A205119.

Programs

Mathematica

s[n_] := s[n] = LucasL[n]; z1 = 500; z2 = 60;
Table[s[n], {n, 1, 30}]    (* A000032 *)
u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]]
Table[u[m], {m, 1, z1}]    (* A205112 *)
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}]     (* A205113 *)
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}]       (* A205114 *)
Table[j[n], {n, 1, z2}]       (* A205115 *)
Table[s[k[n]], {n, 1, z2}]    (* A205116 *)
Table[s[j[n]], {n, 1, z2}]    (* A205117 *)
Table[s[k[n]] - s[j[n]], {n, 1, z2}]     (* A205118 *)
Table[(s[k[n]] - s[j[n]])/n, {n, 1, z2}] (* A205119 *)