A205852 - OEIS

A205852

Numbers k for which 5 divides s(k)-s(j) for some j<k; each k occurs once for each such j; s(k) denotes the (k+1)-st Fibonacci number.

5, 6, 6, 7, 9, 10, 11, 11, 12, 12, 12, 13, 14, 14, 15, 15, 16, 16, 16, 17, 17, 17, 18, 18, 19, 19, 19, 20, 20, 20, 21, 21, 21, 21, 22, 22, 22, 22, 23, 23, 23, 23, 24, 24, 24, 24, 25, 25, 25, 25, 25, 26, 26, 26, 26, 26, 26, 27, 27, 27

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OFFSET

1,1

COMMENTS

For a guide to related sequences, see A205840.

LINKS

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

EXAMPLE

The first six terms match these differences:

s(5)-s(3) = 8-3 = 5

s(6)-s(3) = 13-3 = 10

s(6)-s(5) = 13-8 = 5

s(7)-s(1) = 21-1 = 20

s(9)-s(4) = 55-5 = 50

s(10)-s(8) = 89-34 = 55

MATHEMATICA

s[n_] := s[n] = Fibonacci[n + 1]; z1 = 500; z2 = 60;

f[n_] := f[n] = Floor[(-1 + Sqrt[8 n - 7])/2];

Table[s[n], {n, 1, 30}]

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

Table[u[m], {m, 1, z1}] (* A204922 *)

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] = Delete[w[n], Position[w[n], 0]]

c = 5; t = d[c] (* A205851 *)

k[n_] := k[n] = Floor[(3 + Sqrt[8 t[[n]] - 1])/2]

j[n_] := j[n] = t[[n]] - f[t][[n]] (f[t[[n]]] + 1)/2

Table[k[n], {n, 1, z2}] (* A205852 *)

Table[j[n], {n, 1, z2}] (* A205853 *)

Table[s[k[n]]-s[j[n]], {n, 1, z2}](* A205854 *)

Table[(s[k[n]] - s[j[n]])/c, {n, 1, z2}] (* A205855 *)

CROSSREFS

Cf. A204892, A205855.

Sequence in context: A157729 A335015 A195875 * A028314 A201326 A232247

Adjacent sequences: A205849 A205850 A205851 * A205853 A205854 A205855

KEYWORD

nonn

AUTHOR

Clark Kimberling, Feb 02 2012

STATUS

approved