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

1,1

Links

Table of n, a(n) for n=1..29.

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

Formula

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

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

Example

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

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

Prog

(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

Crossrefs

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

Supersequence of A159611.

Sequence in context: A271041 A270402 A253574 * A238399 A159611 A156585

Adjacent sequences: A343554 A343555 A343556 * A343558 A343559 A343560

Keyword

nonn

Author

Lorenzo Sauras Altuzarra, Apr 28 2021

Extensions

More terms from Michel Marcus, Apr 29 2021

More terms from Amiram Eldar, Apr 29 2021

Status

approved