A053056 Fibonacci numbers whose digit sum is also a Fibonacci number.

0, 1, 2, 3, 5, 8, 21, 233, 317811, 3524578, 7778742049, 259695496911122585, 19740274219868223167, 10284720757613717413913, 263621064469290555679241849789653324393054271110084140201023

Offset: 1

Author

Felice Russo, Feb 25 2000

Keywords

• base
• nonn

Comments

Is this sequence finite?

It is heuristically infinite because of the divergence of the harmonic series. - Charles R Greathouse IV, Sep 20 2012

Examples

			317811 is in the sequence because the sum of its digits 3+1+7+8+1+1=21 is also a Fibonacci number. - Luc Stevens (lms022(AT)yahoo.com), Apr 15 2006
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..24 (all terms < 10^1000).
• Felice Russo, A set of new Smarandache functions, sequences and conjectures in number theory.

Crossrefs

Cf. A000045, A053056, A061268, A053049.

Programs

Maple

with(combinat): F:=[seq(fibonacci(n),n=2..80)]: a:=proc(n) local ff, sod: ff:=convert(fibonacci(n), base,10): sod:=add(ff[i],i=1..nops(ff)): if member(sod,F)=true then fibonacci(n) else fi end: seq(a(n),n=2..300); # Emeric Deutsch, Apr 17 2006

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Oct 03 2000

More terms from Emeric Deutsch, Apr 17 2006

Edited by R. J. Mathar, Aug 08 2008