OFFSET
1,2
COMMENTS
EXAMPLE
The first six terms match these differences:
s(4)-s(2) = 5-2 = 3 = 3*1
s(5)-s(2) = 8-2 = 6 = 3*2
s(5)-s(4) = 8-5 = 3 = 3*1
s(6)-s(1) = 13-1 = 12 = 3*4
s(7)-s(3) = 21-3 = 18 = 3*6
s(8)-s(1) = 34-1 = 33 + 3*11
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 = 3; t = d[c] (* A205841 *)
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}] (* A205842 *)
Table[j[n], {n, 1, z2}] (* A205843 *)
Table[s[k[n]] - s[j[n]], {n, 1, z2}] (* A205844 *)
Table[(s[k[n]] - s[j[n]])/c, {n, 1, z2}] (* A205845 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Feb 01 2012
STATUS
approved