

A254785


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.


1



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, 87, 89, 98, 111, 112, 114, 121, 122, 124, 133, 135, 141, 142, 153, 211, 212, 214, 221, 222, 224, 233, 235, 241, 242, 253, 313, 315, 323, 325, 331, 332, 344, 346, 351, 352, 364, 411, 412, 421
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OFFSET

1,2


COMMENTS

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.


LINKS

Table of n, a(n) for n=1..65.


EXAMPLE

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


PROG

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


CROSSREFS

Cf. A000045, A052382.
Sequence in context: A257671 A285523 A126968 * A126969 A127274 A324280
Adjacent sequences: A254782 A254783 A254784 * A254786 A254787 A254788


KEYWORD

nonn,base,easy


AUTHOR

Derek Orr, Feb 07 2015


STATUS

approved



