%I #6 Feb 23 2015 23:20:00
%S 0,1,2,3,5,8,13,21,34,89,233,6765,701408733,20365011074,
%T 308061521170129,
%U 1777930954809416587147660791784794314784432111526800706093789579403138960940165075820050317562202766948028237512
%N Fibonacci numbers n with digits d_1, d_2, ... d_k such that F(d_1) + F(d_2) + ... + F(d_k) is a Fibonacci number where F(.) is A000045.
%C Excluding 0, this is a subsequence of A254785.
%C The first Fibonacci number that does not satisfy this is 55.
%C The indices of these Fibonacci numbers are 0, 1 (or 2), 3, 4, 5, 6, 7, 8, 9, 11, 13, 20, 44, 51, 71, 534, ...
%e 34 is a Fibonacci number and F(3) + F(4) = 2 + 3 = 5 is also a Fibonacci number. So 34 is a member of this sequence.
%o (PARI) isfib(n)=for(k=0,2*n,if(fibonacci(k)==n,return(1)));0
%o print1(0,", ");for(n=2,10^3,N=fibonacci(n);d=digits(N);s=0;for(i=1,#d,s+=fibonacci(d[i]));if(isfib(s),print1(n,", ")))
%Y Cf. A000045, A254785.
%K nonn,base
%O 1,3
%A _Derek Orr_, Feb 07 2015