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A215367 Lengths of binary representations of prime Fibonacci numbers.

%I A215367 #19 Apr 03 2023 10:36:13
%S A215367 2,2,3,4,7,8,11,15,19,29,32,57,90,94,249,299,300,311,353,394,396,2062,
%T A215367 3278,3739,6463,6718,10018,17745,21352,24991,26041,35290,56815,72833,
%U A215367 90265,102810,139616,275876,301148,409631,412163,419815,646697,728882,892522,1135784,1251758,1366768
%N A215367 Lengths of binary representations of prime Fibonacci numbers.
%C A215367 Some of the larger entries may only correspond to probable primes.
%C A215367 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.
%H A215367 C. K. Caldwell, The Prime Glossary, <a href="https://t5k.org/glossary/page.php?sort=FibonacciPrime">Fibonacci prime</a>
%H A215367 Henri & Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/prptop.php">Probable primes</a>
%F A215367 a(n) = A070939(A005478(n)) = A070939(A000045(A001605(n))).
%e A215367 Tenth prime Fibonacci number is A005478(10) = 433494437, 29 digits in the binary representation, so a(10)=29.
%t A215367 Length /@ IntegerDigits[Select[Fibonacci[Range[1000]], PrimeQ[#] &], 2] (* _T. D. Noe_, Aug 08 2012 *)
%t A215367 IntegerLength[#,2]&/@Select[Fibonacci[Range[1000]],PrimeQ] (* _Harvey P. Dale_, Nov 20 2021 *)
%o A215367 (Java)
%o A215367 import java.math.BigInteger;
%o A215367 public class A215367 {
%o A215367   public static void main (String[] args) {
%o A215367     BigInteger prpr = BigInteger.valueOf(0);
%o A215367     BigInteger prev = BigInteger.valueOf(1), curr;
%o A215367     int indices[] = {
%o A215367     // === insert terms of A001605 here, followed by a comma === //
%o A215367     -1 };
%o A215367     int ipos = 1, ind = indices[0];
%o A215367     for (long k=1; ; ++k) {
%o A215367       if (k==ind) {
%o A215367         System.out.printf("%d, ",prev.bitLength());
%o A215367         ind = indices[ipos++];
%o A215367         if (ind<0) break;
%o A215367       }
%o A215367       curr = prpr.add(prev);
%o A215367       prpr = prev;
%o A215367       prev = curr;
%o A215367     }
%o A215367   }
%o A215367 }
%Y A215367 Cf. A005478, A020909.
%K A215367 nonn,base
%O A215367 1,1
%A A215367 _Alex Ratushnyak_, Aug 08 2012