login
A159611
Indices of the Fermat primes in the sequence of primes.
9
2, 3, 7, 55, 6543
OFFSET
1,1
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
FORMULA
A098006(a(n)) = 0. - Reinhard Zumkeller, Mar 26 2013
a(n) = A000720(A019434(n)). - Michel Marcus, Apr 29 2021
EXAMPLE
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.
MATHEMATICA
PrimePi/@{3, 5, 17, 257, 65537} (* Harvey P. Dale, Aug 07 2022 *)
PROG
(Haskell)
import Data.List (elemIndices)
a159611 n = a159611_list !! (n-1)
a159611_list = map (+ 2) $ elemIndices 0 a098006_list
-- Reinhard Zumkeller, Mar 26 2013
(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
CROSSREFS
Cf. A000040 (primes), A000720, A019434 (Fermat primes).
Cf. A098006.
Sequence in context: A253574 A343557 A238399 * A156585 A354744 A299923
KEYWORD
nonn,hard
AUTHOR
Walter Nissen, Apr 16 2009
EXTENSIONS
Name edited by Felix Fröhlich, Apr 30 2021
STATUS
approved