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A205847 Numbers k for which 4 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
4, 6, 6, 7, 7, 7, 8, 9, 10, 10, 10, 10, 11, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 14, 14, 15, 15, 16, 16, 16, 16, 16, 16, 16, 17, 17, 18, 18, 18, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 19, 19, 19, 19, 20, 20, 20, 21, 21, 21 (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(4)-s(1) = 5-1 = 4

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

s(6)-s(4) = 13-5 = 8

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

s(7)-s(4) = 21-5 = 16

s(7)-s(6) = 21-13 = 8

MATHEMATICA

s[n_] := s[n] = Fibonacci[n + 1]; z1 = 400; 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 = 4; t = d[c]    (* A205846 *)

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}]    (* A205847 *)

Table[j[n], {n, 1, z2}]    (* A205848 *)

Table[s[k[n]] - s[j[n]], {n, 1, z2}] * A205849 *)

Table[(s[k[n]] - s[j[n]])/c, {n, 1, z2}] (* A205850 *)

CROSSREFS

Cf. A204892, A205850.

Sequence in context: A035551 A087573 A201235 * A227967 A292672 A018937

Adjacent sequences:  A205844 A205845 A205846 * A205848 A205849 A205850

KEYWORD

nonn

AUTHOR

Clark Kimberling, Feb 02 2012

STATUS

approved

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Last modified July 31 05:53 EDT 2021. Contains 346367 sequences. (Running on oeis4.)