|
|
A205865
|
|
[s(k)-s(j)]/7, where the pairs (k,j) are given by A205862 and A205863, and s(k) denotes the (k+1)-st Fibonacci number.
|
|
3
|
|
|
1, 3, 6, 3, 12, 33, 52, 49, 46, 87, 86, 138, 228, 227, 141, 369, 368, 282, 141, 597, 564, 966, 1563, 1551, 2530, 2529, 2443, 2302, 2161, 4092, 4089, 4086, 4040, 6621, 6483, 10716, 10713, 10710, 10664, 6624, 17340, 17337, 17334, 17288, 13248
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
For a guide to related sequences, see A205840.
|
|
LINKS
|
|
|
EXAMPLE
|
The first six terms match these differences:
s(5)-s(1) = 8-1 = 7 = 7*1
s(8)-s(6) = 34-13 = 21 = 7*3
s(9)-s(6) = 55-13 = 42 = 7*6
s(9)-s(8) = 55-34 = 21 = 7*3
s(10)-s(4) = 89-5 = 84 = 7*12
s(13)-s(6) = 377-13 = 364 =7*52
|
|
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]]
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}] (* A205862 *)
Table[j[n], {n, 1, z2}] (* A205863 *)
Table[s[k[n]] - s[j[n]], {n, 1, z2}] (* A205864 *)
Table[(s[k[n]]-s[j[n]])/c, {n, 1, z2}] (* A205865 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|