A023395 Only Fermat number divisible by A023394(n) is 2^2^a(n) + 1.

0, 1, 2, 3, 5, 4, 12, 6, 11, 11, 9, 5, 18, 12, 10, 12, 23, 16, 15, 10, 19, 12, 19, 13, 36, 21, 38, 32, 25, 17, 39, 6, 26, 27, 30, 30, 8, 12, 15, 29, 38, 7, 25, 27, 36, 42, 25, 13, 13, 55

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

Table of n, a(n) for n=1..50.

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).

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

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

Cf. A000215, A023394, A046052.

Sequence in context: A193971 A258861 A171038 * A316655 A318848 A193798

Adjacent sequences: A023392 A023393 A023394 * A023396 A023397 A023398

Keyword

nonn,more

Author

David W. Wilson

Extensions

a(25)-a(41) computed using data from Wilfrid Keller by T. D. Noe, Feb 01 2009

Three more terms by T. D. Noe, Feb 03 2009

Six more terms from Wilfrid Keller by T. D. Noe, Jan 14 2013

Status

approved