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A205877 Numbers k for which 10 divides s(k)-s(j) for some j each k occurs once for each such j; s(k) denotes the (k+1)-st Fibonacci number.

%I A205877 #5 Mar 30 2012 18:58:12
%S A205877 6,7,9,11,12,12,15,16,16,17,17,18,18,19,19,21,21,21,22,22,22,23,24,24,
%T A205877 24,25,25,25,26,26,27,27,27,27,28,29,30,30,31,31,31,32,32,32,33,33,33,
%U A205877 33,34,34
%N A205877 Numbers k for which 10 divides s(k)-s(j) for some j<k; each k occurs once for each such j; s(k) denotes the (k+1)-st Fibonacci number.
%C A205877 For a guide to related sequences, see A205840.
%e A205877 The first three terms match these differences:
%e A205877 s(6)-s(3) = 13-3 = 10 = 10*1
%e A205877 s(7)-s(1) = 21-1 = 20 = 10*2
%e A205877 s(9)-s(4) = 55-5 = 50 = 10*5
%t A205877 s[n_] := s[n] = Fibonacci[n + 1]; z1 = 600; z2 = 50;
%t A205877 f[n_] := f[n] = Floor[(-1 + Sqrt[8 n - 7])/2];
%t A205877 Table[s[n], {n, 1, 30}]
%t A205877 u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]]
%t A205877 Table[u[m], {m, 1, z1}]     (* A204922 *)
%t A205877 v[n_, h_] := v[n, h] = If[IntegerQ[u[h]/n], h, 0]
%t A205877 w[n_] := w[n] = Table[v[n, h], {h, 1, z1}]
%t A205877 d[n_] := d[n] = Delete[w[n], Position[w[n], 0]]
%t A205877 c = 10; t = d[c]    (* A205876 *)
%t A205877 k[n_] := k[n] = Floor[(3 + Sqrt[8 t[[n]] - 1])/2]
%t A205877 j[n_] := j[n] = t[[n]] - f[t][[n]] (f[t[[n]]] + 1)/2
%t A205877 Table[k[n], {n, 1, z2}]     (* A205877 *)
%t A205877 Table[j[n], {n, 1, z2}]      (* A205878 *)
%t A205877 Table[s[k[n]] - s[j[n]], {n, 1, z2}] (* A205879 *)
%t A205877 Table[(s[k[n]] - s[j[n]])/c, {n, 1, z2}]  (* A205880 *)
%Y A205877 Cf. A204892, A205878, A205880.
%K A205877 nonn
%O A205877 1,1
%A A205877 _Clark Kimberling_, Feb 02 2012