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A205857 Numbers k for which 6 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
5, 6, 7, 9, 9, 10, 12, 12, 13, 13, 13, 14, 15, 15, 16, 16, 16, 17, 17, 18, 18, 18, 18, 19, 19, 19, 20, 20, 21, 21, 21, 21, 21, 22, 22, 22, 22, 23, 24, 24, 24, 24, 24, 25, 25, 25, 25, 25, 25, 26, 26, 26, 27, 27, 27, 27, 28, 28, 28, 28 (list; graph; refs; listen; history; text; internal format)
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(2) = 8-2 = 6 = 6*1

s(6)-s(1) = 13-1 = 12 = 6*2

s(7)-s(3) = 21-3 = 18 = 6*3

s(9)-s(1) = 55-1 = 54 = 6*9

s(9)-s(6) = 55-13 = 42 = 6*7

s(10)-s(4) = 89-5 = 84 =6*14

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 = 6; t = d[c]    (* A205856 *)

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}]     (* A205857 *)

Table[j[n], {n, 1, z2}]     (* A205858 *)

Table[s[k[n]]-s[j[n]], {n, 1, z2}]    (* A205859 *)

Table[(s[k[n]]-s[j[n]])/c, {n, 1, z2}]  (* A205860 *)

CROSSREFS

Cf. A204892, A205857, A205860.

Sequence in context: A320021 A081407 A268857 * A196026 A191850 A066263

Adjacent sequences:  A205854 A205855 A205856 * A205858 A205859 A205860

KEYWORD

nonn

AUTHOR

Clark Kimberling, Feb 02 2012

STATUS

approved

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Last modified July 12 13:27 EDT 2020. Contains 335663 sequences. (Running on oeis4.)