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A215367 Lengths of binary representations of prime Fibonacci numbers. 2
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 (list; graph; refs; listen; history; text; internal format)
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 *)

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

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Last modified June 25 11:48 EDT 2017. Contains 288709 sequences.