A118113 - OEIS

%I #23 Jan 03 2017 23:54:30

%S 1,3,5,9,11,17,19,21,33,35,37,41,43,65,67,69,73,75,81,83,85,129,131,

%T 133,137,139,145,147,149,161,163,165,169,171,257,259,261,265,267,273,

%U 275,277,289,291,293,297,299,321,323,325,329,331,337,339,341,513,515,517

%N Even Fibbinary numbers + 1; also 2*Fibbinary(n) + 1.

%C a(n) = A022340(n) + 1 = 2*A003714(n) + 1.

%H Alois P. Heinz, <a href="/A118113/b118113.txt">Table of n, a(n) for n = 0..1000</a>

%F Solutions to {x : binomial(3x,x) mod (x+1) != 0 } are given in A022341. The corresponding values of binomial(3x,x) mod (x+1) are given here.

%p F:= combinat[fibonacci]:

%p b:= proc(n) local j;

%p       if n=0 then 0

%p     else for j from 2 while F(j+1)<=n do od;

%p          b(n-F(j))+2^(j-2)

%p       fi

%p     end:

%p a:= n-> 2*b(n)+1:

%p seq(a(n), n=0..70);  # _Alois P. Heinz_, Aug 03 2012

%t Select[Table[Mod[Binomial[3*k,k], k+1], {k,1200}], #>0&]

%Y Cf. A000108, A118112, A022341.

%Y Cf. A003714 (Fibbinary numbers), A022340 (even Fibbinary numbers).

%Y Cf. A263190, A171791, A263075.

%K nonn

%O 0,2

%A _Labos Elemer_, Apr 13 2006

%E New definition from _T. D. Noe_, Dec 19 2006