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A205850 [s(k)-s(j)]/4, where the pairs (k,j) are given by A205847 and A205848, and s(k) denotes the (k+1)-st Fibonacci number. 5
1, 3, 2, 5, 4, 2, 8, 13, 22, 21, 19, 17, 34, 58, 57, 55, 53, 36, 94, 93, 91, 89, 72, 36, 152, 144, 246, 233, 399, 398, 396, 394, 377, 341, 305, 644, 610, 1045, 1044, 1042, 1040, 1023, 987, 951, 646, 1691, 1690, 1688, 1686, 1669, 1633, 1597, 1292, 646 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

For a guide to related sequences, see A205840.

LINKS

Table of n, a(n) for n=1..54.

EXAMPLE

The first six terms match these differences:

s(4)-s(1) = 5-1 = 4 = 4*1

s(6)-s(1) = 13-1 = 12= 4*3

s(6)-s(4) = 13-5 = 8 = 4*2

s(7)-s(1) = 21-1 = 20 = 4*5

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

s(7)-s(6) = 21-13 = 8 = 4*2

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, A205845, A205849.

Sequence in context: A110661 A143124 A205400 * A204890 A307775 A239680

Adjacent sequences:  A205847 A205848 A205849 * A205851 A205852 A205853

KEYWORD

nonn

AUTHOR

Clark Kimberling, Feb 02 2012

STATUS

approved

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Last modified May 18 23:31 EDT 2022. Contains 353826 sequences. (Running on oeis4.)