A254786 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.

0, 1, 2, 3, 5, 8, 13, 21, 34, 89, 233, 6765, 701408733, 20365011074, 308061521170129, 1777930954809416587147660791784794314784432111526800706093789579403138960940165075820050317562202766948028237512

Offset

1,3

Comments

Excluding 0, this is a subsequence of A254785.

The first Fibonacci number that does not satisfy this is 55.

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, ...

Links

Table of n, a(n) for n=1..16.

Example

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.

Prog

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

Crossrefs

Cf. A000045, A254785.

Sequence in context: A302019 A207976 A093332 * A050762 A321656 A005170

Adjacent sequences: A254783 A254784 A254785 * A254787 A254788 A254789

Keyword

nonn,base

Author

Derek Orr, Feb 07 2015

Status

approved