A215367 Lengths of binary representations of prime Fibonacci numbers.

2, 2, 3, 4, 7, 8, 11, 15, 19, 29, 32, 57, 90, 94, 249, 299, 300, 311, 353, 394, 396, 2062, 3278, 3739, 6463, 6718, 10018, 17745, 21352, 24991, 26041, 35290, 56815, 72833, 90265, 102810, 139616, 275876, 301148, 409631, 412163, 419815, 646697, 728882, 892522, 1135784, 1251758, 1366768

Offset

1,1

Comments

Some of the larger entries may only correspond to probable primes.

As of August 2012, the index of last provable Fibonacci prime is A001605(33)=81839, that is, a(n) corresponds to a probable prime for n>33.

Links

Table of n, a(n) for n=1..48.

C. K. Caldwell, The Prime Glossary, Fibonacci prime

Henri & Renaud Lifchitz, Probable primes

Formula

a(n) = A070939(A005478(n)) = A070939(A000045(A001605(n))).

Example

Tenth prime Fibonacci number is A005478(10) = 433494437, 29 digits in the binary representation, so a(10)=29.

Mathematica

Length /@ IntegerDigits[Select[Fibonacci[Range[1000]], PrimeQ[#] &], 2] (* T. D. Noe, Aug 08 2012 *)
IntegerLength[#, 2]&/@Select[Fibonacci[Range[1000]], PrimeQ] (* Harvey P. Dale, Nov 20 2021 *)

Prog

(Java)
import java.math.BigInteger;
public class A215367 {
  public static void main (String[] args) {
    BigInteger prpr = BigInteger.valueOf(0);
    BigInteger prev = BigInteger.valueOf(1), curr;
    int indices[] = {
    // === insert terms of A001605 here, followed by a comma === //
    -1 };
    int ipos = 1, ind = indices[0];
    for (long k=1; ; ++k) {
      if (k==ind) {
        System.out.printf("%d, ", prev.bitLength());
        ind = indices[ipos++];
        if (ind<0) break;
      }
      curr = prpr.add(prev);
      prpr = prev;
      prev = curr;
    }
  }
}

Crossrefs

Cf. A005478, A020909.

Sequence in context: A086969 A014692 A058670 * A276526 A091605 A145468

Adjacent sequences: A215364 A215365 A215366 * A215368 A215369 A215370

Keyword

nonn,base

Author

Alex Ratushnyak, Aug 08 2012

Status

approved