OFFSET

1,3

COMMENTS

From Jianing Song, Mar 02 2021: (Start)

2^(a(n)+1) is the multiplicative order of 2 modulo A023394(n).

Each k occurs A046052(k) times in this sequence provided that F(k) = 2^2^k + 1 is squarefree (no counterexamples are known). (End)

Alternatively, a(n) is the only k such that A023394(n) divides A000215(k). - Lorenzo Sauras Altuzarra, Feb 01 2023

LINKS

Wilfrid Keller, Prime factors k.2^n + 1 of Fermat numbers F_m

Lorenzo Sauras-Altuzarra, Some properties of the factors of Fermat numbers, Art Discrete Appl. Math. (2022).

PROG

(PARI) forprime(p=3, , r=znorder(Mod(2, p)); hammingweight(r)==1&&print1(logint(r, 2)-1, ", ")) \\ Jeppe Stig Nielsen, Mar 04 2018

CROSSREFS

KEYWORD

nonn,more

AUTHOR

EXTENSIONS

STATUS

approved