A343557 Indices of the prime factors of Fermat numbers in the sequence of primes.

2, 3, 7, 55, 116, 6543, 10847, 23974, 27567, 76709, 177975, 457523, 887643, 1625567, 2751966, 3772007, 9385401, 42401669, 61136051, 301137372, 2946723445, 7632981296, 24728168164, 98261951745, 99582868271, 159657063059, 231641062432, 851793186025, 870658222248

Offset: 1

Author

Lorenzo Sauras Altuzarra, Apr 28 2021

Keywords

• nonn

Examples

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..50
• Index entries for sequences that are related to primes dividing Fermat numbers.

Crossrefs

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

Supersequence of A159611.

Programs

Maple

q:=n->(irem(2^(2^padic:-ordp(ithprime(n)-1, 2))-1, ithprime(n)) = 0):
select(q, [$1..10^5])[]; # Lorenzo Sauras Altuzarra, Feb 20 2023

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
my(i=1); forprime(p=1, , if(is_a023394(p), print1(i, ", ")); i++) \\ Felix Fröhlich, Apr 30 2021

Formula

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

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

Extensions

More terms from Michel Marcus, Apr 29 2021

More terms from Amiram Eldar, Apr 29 2021