A205875 [s(k)-s(j)]/9, where the pairs (k,j) are given by A205872 and A205873, and s(k) denotes the (k+1)-st Fibonacci number.
2, 6, 9, 25, 16, 41, 32, 16, 64, 176, 287, 281, 464, 642, 1216, 1967, 1958, 1942, 1926, 3184, 3178, 2897, 5136, 8336, 8330, 8049, 5152, 13488, 13482, 13201, 10304, 5152, 21824, 20608, 35312, 35310, 57136, 56672, 92448, 92439, 92423, 92407
Offset: 1
Keywords
Examples
The first six terms match these differences: s(7)-s(3) = 21-3 = 18 = 9*2 s(9)-s(1) = 55-1 = 54 = 9*6 s(10)-s(5) = 89-8 = 81 = 9*9 s(12)-s(5) = 233-8 = 225 = 9*25 s(12)-s(10) = 233-89 = 144 = 9*16 s(13)-s(5) = 377-8 = 369 =9*41
Programs
-
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 = 9; t = d[c] (* A205871 *) 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}] (* A205872 *) Table[j[n], {n, 1, z2}] (* A205873 *) Table[s[k[n]] - s[j[n]], {n, 1, z2}] (* A205874 *) Table[(s[k[n]] - s[j[n]])/c, {n, 1, z2}] (* A205875 *)
Comments