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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 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

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Last modified December 9 02:53 EST 2021. Contains 349625 sequences. (Running on oeis4.)