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%I #14 Nov 12 2024 22:17:22
%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,my(d=digits(n));if(vecsort(d,,8)[1], my(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