A254785 - OEIS

%I #9 Feb 23 2015 23:19:29

%S 1,2,3,4,5,6,7,8,9,11,12,13,21,22,23,31,32,34,43,45,54,56,65,67,76,78,

%T 87,89,98,111,112,114,121,122,124,133,135,141,142,153,211,212,214,221,

%U 222,224,233,235,241,242,253,313,315,323,325,331,332,344,346,351,352,364,411,412,421

%N Zeroless 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 If n is a member of this sequence, any reordering of its digits is also a member of this sequence. Since A000045(0) = 0, any number is the sequence can have an arbitrary number of zeros; hence, the numbers with zeros have been omitted as trivial.

%e 23 is a member of this sequence because F(2) + F(3) = 1+2 = 3 is a Fibonacci number.

%o (PARI) isfib(n)=for(k=0,2*n,if(fibonacci(k)==n,return(1)));0

%o for(n=1,10^3,d=digits(n);if(vecsort(d,,8)[1],s=0;for(i=1,#d,s+=fibonacci(d[i]));if(isfib(s),print1(n,", ")))

%Y Cf. A000045, A052382.

%K nonn,base,easy

%O 1,2

%A _Derek Orr_, Feb 07 2015