A205114 Least k such that n divides L(k)-L(j) for some j satisfying 1<=j<k, where L(j) is the j-th Lucas number (A000032).

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

1,1

Comments

See A204892 for a discussion and guide to related sequences.

Links

Table of n, a(n) for n=1..60.

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 *)

Crossrefs

Cf. A000032, A204892, A205119.

Sequence in context: A031233 A030584 A030564 * A293428 A281487 A224401

Adjacent sequences: A205111 A205112 A205113 * A205115 A205116 A205117

Keyword

nonn

Author

Clark Kimberling, Jan 22 2012

Status

approved