A163113 Fibonacci numbers containing equal numbers of prime digits and nonprime digits.

13, 21, 34, 1597, 2584, 6765, 121393, 514229, 14930352, 24157817, 7778742049, 365435296162, 44945570212853, 184551825793033096366333, 781774079430987230203437, 7896325826131730509282738943634332893686268675876375

Offset

1,1

Comments

It is obvious that these numbers must contain an even number of digits.

This sequence is probably finite. The equivalent sequences in bases 4, 6, and 8 are probably infinite. - Franklin T. Adams-Watters, Aug 06 2009

Links

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

Simon Plouffe, Project Gutenberg

Example

24157817 is a Fibonacci number containing equal numbers of prime digits (2,5,7,7) and nonprime digits (4,1,8,1).

Mathematica

pnpQ[n_]:=Module[{idn=IntegerDigits[n], len}, len=Length[idn]; EvenQ[len] && Count[idn, _?PrimeQ]==len/2]; Select[Fibonacci[Range[250]], pnpQ] (* Harvey P. Dale, May 01 2012 *)

Prog

(PARI) (digits(n, b=10)=local(r); r=[]; while(n>0, r=concat([n%b], r); n\=b); r); for(n=1, 500, v=digits(fibonacci(n)); np=sum(i=1, #v, isprime(v[i])); if(#v==2*np, print1(fibonacci(n)", ")))

Crossrefs

Cf. A000045.

Sequence in context: A164451 A164432 A034292 * A164496 A164459 A164453

Adjacent sequences: A163110 A163111 A163112 * A163114 A163115 A163116

Keyword

nonn,base

Author

Parthasarathy Nambi, Jul 21 2009

Extensions

Edited and extended by Franklin T. Adams-Watters, Aug 06 2009

Status

approved