A205442 - OEIS

A205442

Least k such that n divides s(k)-s(j) for some j<k, where s(j) is the (2j-1)-st Fibonacci number.

2, 3, 3, 3, 6, 4, 5, 4, 7, 7, 4, 4, 8, 6, 11, 5, 10, 7, 6, 7, 5, 6, 13, 7, 26, 9, 19, 6, 5, 12, 9, 5, 5, 10, 21, 7, 20, 6, 15, 16, 11, 6, 23, 6, 31, 13, 9, 7, 29, 27, 19, 9, 28, 19, 6, 13, 7, 7, 16, 12

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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

s[n_] := s[n] = Fibonacci[2*n - 1]; z1 = 500; z2 = 60;

Table[s[n], {n, 1, 30}] (* A001519 *)

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

Table[u[m], {m, 1, z1}] (* A205371 *)

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}] (* A205441 *)

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}] (* A205442 *)

Table[j[n], {n, 1, z2}] (* A205443 *)

Table[s[k[n]], {n, 1, z2}] (* A205444 *)

Table[s[j[n]], {n, 1, z2}] (* A205445 *)

Table[s[k[n]] - s[j[n]], {n, 1, z2}] (* A205446 *)

Table[(s[k[n]] - s[j[n]])/n, {n, 1, z2}] (* A205447 *)

CROSSREFS

Cf. A001519, A205447, A204892.

Sequence in context: A126854 A115206 A093653 * A049982 A245642 A289559

Adjacent sequences: A205439 A205440 A205441 * A205443 A205444 A205445

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jan 27 2012

STATUS

approved