A360469 Only k >= 0 such that, for every odd r > 0, A093179(n) divides the generalized Fermat number (A007117(n)^r)^(2^k) + 1.

3, 3, 5, 3, 7, 7, 9, 8, 11, 11, 13, 10, 15, 15, 17, 16, 19, 19, 21, 19, 23, 23, 25, 24, 27, 27, 29, 25, 31, 31, 33, 32, 35, 35, 37, 35, 39, 39, 41, 40, 43, 43, 45, 42, 47, 47, 49, 48, 51, 51, 53, 51, 55, 55, 57, 56, 59, 59, 61, 56, 63, 63, 65, 64, 67, 67, 69, 67, 71, 71, 73, 72, 75, 75, 77, 74, 79

Offset: 3

Author

Lorenzo Sauras Altuzarra, Feb 27 2023

Keywords

• nonn
• easy

Examples

			A093179(5) = 641, A007117(5) = 5 and the only k >= 0 such that, for every odd r > 0, 641 divides the generalized Fermat number (5^r)^(2^k) + 1 is 5; so a(5) = 5.
		

Links

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

Crossrefs

Cf. A000215 (Fermat numbers), A007117, A007814 (dyadic valuation), A093179, A307843 (divisors of Fermat numbers).

Programs

Maple

a:=n->n-padic:-ordp(n+2,2):
seq(a(n), n=3..79);

PARI

a(n) = n - valuation(n+2, 2);
vector(77,n,a(n+2)) \\ Joerg Arndt, Mar 03 2023

Formula

a(n) = n - A007814(n + 2) (due to Jinyuan Wang).