A159611 Indices of the Fermat primes in the sequence of primes.

2, 3, 7, 55, 6543

Offset: 1

Author

Walter Nissen, Apr 16 2009

Keywords

• nonn
• hard

Comments

If it exists, a(6) >= primepi(2^(2^33)+1) which has more than 2*10^9 decimal digits. - Amiram Eldar, Sep 27 2024

Examples

			3, the 1st Fermat prime is the 2nd prime, so a(1) = 2.
17, the 3rd Fermat prime is the 7th prime, so a(3) = 7.
		

Links

• Index entries for sequences that are related to primes dividing Fermat numbers.

Crossrefs

Cf. A000040 (primes), A000720, A019434 (Fermat primes).

Cf. A098006.

Programs

Haskell

import Data.List (elemIndices)
a159611 n = a159611_list !! (n-1)
a159611_list = map (+ 2) $ elemIndices 0 a098006_list
-- Reinhard Zumkeller, Mar 26 2013

Mathematica

PrimePi/@{3,5,17,257,65537} (* Harvey P. Dale, Aug 07 2022 *)

PARI

for(i=0, 10, isprime(f=2^2^i+1) & print1(primepi(f), ", ")) \\ Michel Marcus, Apr 28 2016

PARI

a152155(n) = centerlift(Mod(3, 2^(2^n)+1)^(2^(2^n-1)))
print1(2, ", "); for(x=0, oo, if(a152155(x)==-1, print1(primepi(2^(2^x)+1), ", "))) \\ Felix Fröhlich, Apr 30 2021

Formula

A098006(a(n)) = 0. - Reinhard Zumkeller, Mar 26 2013

a(n) = A000720(A019434(n)). - Michel Marcus, Apr 29 2021

Extensions

Name edited by Felix Fröhlich, Apr 30 2021