OFFSET
1,2
COMMENTS
For a guide to related sequences, see A205840.
EXAMPLE
The first six terms match these differences:
s(6)-s(4) = 13-5 = 8 = 8*1
s(7)-s(4) = 21-5 = 16 = 8*2
s(7)-s(6) = 21-13 = 8 = 8*1
s(8)-s(2) = 34-2 = 32 = 8*4
s(10)-s(1) = 89-1 = 88 = 8*11
s(11)-s(5) = 144-8 = 136 =8*17
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 = 8; t = d[c] (* A205866 *)
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}] (* A205867 *)
Table[j[n], {n, 1, z2}] (* A205868 *)
Table[s[k[n]] - s[j[n]], {n, 1, z2}] (* A205869 *)
Table[(s[k[n]] - s[j[n]])/c, {n, 1, z2}] (* A205870 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Feb 02 2012
STATUS
approved