A343557 - OEIS

%I #36 Sep 06 2024 15:16:28

%S 2,3,7,55,116,6543,10847,23974,27567,76709,177975,457523,887643,

%T 1625567,2751966,3772007,9385401,42401669,61136051,301137372,

%U 2946723445,7632981296,24728168164,98261951745,99582868271,159657063059,231641062432,851793186025,870658222248

%N Indices of the prime factors of Fermat numbers in the sequence of primes.

%H Amiram Eldar, <a href="/A343557/b343557.txt">Table of n, a(n) for n = 1..50</a>

%H <a href="/index/Pri">Index entries for sequences that are related to primes dividing Fermat numbers</a>.

%F a(n) = A000720(A023394(n)).

%F A000040(a(n)) = A023394(n).

%e A000040(a(5)) = A000040(116) = 641 = A023394(5).

%p q:=n->(irem(2^(2^padic:-ordp(ithprime(n)-1, 2))-1, ithprime(n)) = 0):

%p select(q, [$1..10^5])[]; # _Lorenzo Sauras Altuzarra_, Feb 20 2023

%o (PARI) is_a023394(p)=p>2 && Mod(2,p)^lift(Mod(2,znorder(Mod(2,p)))^p)==1 && isprime(p) \\ after _Charles R Greathouse IV_ in A023394

%o my(i=1); forprime(p=1, , if(is_a023394(p), print1(i, ", ")); i++) \\ _Felix Fröhlich_, Apr 30 2021

%Y Cf. A000040 (primes), A000720 (primepi), A023394 (prime factors of Fermat primes).

%Y Supersequence of A159611.

%K nonn

%O 1,1

%A _Lorenzo Sauras Altuzarra_, Apr 28 2021

%E More terms from _Michel Marcus_, Apr 29 2021

%E More terms from _Amiram Eldar_, Apr 29 2021