This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A159611 #38 Sep 27 2024 07:22:06
%S A159611 2,3,7,55,6543
%N A159611 Indices of the Fermat primes in the sequence of primes.
%C A159611 If it exists, a(6) >= primepi(2^(2^33)+1) which has more than 2*10^9 decimal digits. - _Amiram Eldar_, Sep 27 2024
%H A159611 <a href="/index/Pri">Index entries for sequences that are related to primes dividing Fermat numbers</a>.
%F A159611 A098006(a(n)) = 0. - _Reinhard Zumkeller_, Mar 26 2013
%F A159611 a(n) = A000720(A019434(n)). - _Michel Marcus_, Apr 29 2021
%e A159611 3, the 1st Fermat prime is the 2nd prime, so a(1) = 2.
%e A159611 17, the 3rd Fermat prime is the 7th prime, so a(3) = 7.
%t A159611 PrimePi/@{3,5,17,257,65537} (* _Harvey P. Dale_, Aug 07 2022 *)
%o A159611 (Haskell)
%o A159611 import Data.List (elemIndices)
%o A159611 a159611 n = a159611_list !! (n-1)
%o A159611 a159611_list = map (+ 2) $ elemIndices 0 a098006_list
%o A159611 -- _Reinhard Zumkeller_, Mar 26 2013
%o A159611 (PARI) for(i=0, 10, isprime(f=2^2^i+1) & print1(primepi(f), ", ")) \\ _Michel Marcus_, Apr 28 2016
%o A159611 (PARI) a152155(n) = centerlift(Mod(3, 2^(2^n)+1)^(2^(2^n-1)))
%o A159611 print1(2, ", "); for(x=0, oo, if(a152155(x)==-1, print1(primepi(2^(2^x)+1), ", "))) \\ _Felix Fröhlich_, Apr 30 2021
%Y A159611 Cf. A000040 (primes), A000720, A019434 (Fermat primes).
%Y A159611 Cf. A098006.
%K A159611 nonn,hard
%O A159611 1,1
%A A159611 _Walter Nissen_, Apr 16 2009
%E A159611 Name edited by _Felix Fröhlich_, Apr 30 2021