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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. 9
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 15 00:00 EDT 2021. Contains 345041 sequences. (Running on oeis4.)