A205877 Numbers k for which 10 divides s(k)-s(j) for some j

6, 7, 9, 11, 12, 12, 15, 16, 16, 17, 17, 18, 18, 19, 19, 21, 21, 21, 22, 22, 22, 23, 24, 24, 24, 25, 25, 25, 26, 26, 27, 27, 27, 27, 28, 29, 30, 30, 31, 31, 31, 32, 32, 32, 33, 33, 33, 33, 34, 34

Offset: 1

Author

Clark Kimberling, Feb 02 2012

Keywords

• nonn

Comments

For a guide to related sequences, see A205840.

Examples

			The first three terms match these differences:
s(6)-s(3) = 13-3 = 10 = 10*1
s(7)-s(1) = 21-1 = 20 = 10*2
s(9)-s(4) = 55-5 = 50 = 10*5
		

Crossrefs

Cf. A204892, A205878, A205880.

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 = 10; t = d[c]    (* A205876 *)
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}]     (* A205877 *)
Table[j[n], {n, 1, z2}]      (* A205878 *)
Table[s[k[n]] - s[j[n]], {n, 1, z2}] (* A205879 *)
Table[(s[k[n]] - s[j[n]])/c, {n, 1, z2}]  (* A205880 *)