A205450 - OEIS

A205450

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

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

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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

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

See A204892 for a discussion and guide to related sequences.

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 *)

CROSSREFS

Cf. A001906, A205455, A204892.

Sequence in context: A324662 A024222 A196063 * A215674 A279211 A110545

Adjacent sequences: A205447 A205448 A205449 * A205451 A205452 A205453

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jan 27 2012

STATUS

approved