A205877 - OEIS

A205877

Numbers k for which 10 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.

6, 7, 9, 11, 12, 12, 15, 16, 16, 17, 17, 18, 18, 19, 19, 21, 21, 21, 22, 22, 22, 23, 24, 24, 24, 25, 25, 25, 26, 26, 27, 27, 27, 27, 28, 29, 30, 30, 31, 31, 31, 32, 32, 32, 33, 33, 33, 33, 34, 34

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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..50.

EXAMPLE

The first three terms match these differences:

s(6)-s(3) = 13-3 = 10 = 10*1

s(7)-s(1) = 21-1 = 20 = 10*2

s(9)-s(4) = 55-5 = 50 = 10*5

MATHEMATICA

s[n_] := s[n] = Fibonacci[n + 1]; z1 = 600; z2 = 50;

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 = 10; t = d[c] (* A205876 *)

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}] (* A205877 *)

Table[j[n], {n, 1, z2}] (* A205878 *)

Table[s[k[n]] - s[j[n]], {n, 1, z2}] (* A205879 *)

Table[(s[k[n]] - s[j[n]])/c, {n, 1, z2}] (* A205880 *)

CROSSREFS

Cf. A204892, A205878, A205880.

Sequence in context: A216361 A216360 A339928 * A081053 A022892 A120164

Adjacent sequences: A205874 A205875 A205876 * A205878 A205879 A205880

KEYWORD

nonn

AUTHOR

Clark Kimberling, Feb 02 2012

STATUS

approved