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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
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
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
Sequence in context: A086969 A014692 A058670 * A276526 A091605 A145468
KEYWORD
nonn,base
AUTHOR
Alex Ratushnyak, Aug 08 2012
STATUS
approved