A122276 If b(n-1) + b(n-2) < n then a(n) = 0, otherwise a(n) = 1, where b(i) = A096535(i).

1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1

Offset: 2

Author

Klaus Brockhaus, Aug 29 2006

Keywords

• nonn

Comments

Conjecture: lim {n -> infinity} x_n / y_n = 1, where x_n is the number of j <= n such that A096535(j) = A096535(j-1) + A096535(j-2) and y_n is the number of j <= n such that A096535(j) = A096535(j-1) + A096535(j-2) - j. Computational support: x_n / y_n = 0.9999917 for n = 10^9.

Links

• G. C. Greubel, Table of n, a(n) for n = 2..1000

Crossrefs

Cf. A096535, A122277.

Programs

Mathematica

f[s_] := f[s] = Append[s, Mod[s[[ -2]] + s[[ -1]], Length[s]]]; t = Nest[f, {1, 1}, 106]; s = {}; Do[AppendTo[s, If[t[[n]] + t[[n + 1]] < n + 1, 0, 1]], {n, 105}]; s (* Robert G. Wilson v Sep 02 2006 *)

PARI

{m=107;a=1;b=1;for(n=2,m,d=divrem(a+b,n);print1(d[1],",");a=b;b=d[2])}

Formula

a(n) = floor((A096535(n-1)+A096535(n-2))/n)