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, 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

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