A205837
Numbers k for which 2 divides s(k)-s(j) for some j
3, 4, 4, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16
Offset: 1
Keywords
Examples
The first six terms match these differences: s(3)-s(1) = 3-1 = 2 s(4)-s(1) = 5-1 = 4 s(4)-s(3) = 5-3 = 2 s(5)-s(2) = 8-2 = 6 s(6)-s(1) = 13-1 = 12 s(6)-s(3) = 13-3 = 10
Programs
-
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 = 2; t = d[c] (* A205556 *) 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}] (* A205837 *) Table[j[n], {n, 1, z2}] (* A205838 *) Table[s[k[n]] - s[j[n]], {n, 1, z2}](* A205839 *) Table[(s[k[n]] - s[j[n]])/c, {n, 1, z2}](* A205840 *)
Comments