A344185 a(n) = A344141(n) - 2^n.

0, 3, 3, 3, 5, 3, 3, 27, 3, 9, 5, 9, 27, 33, 3, 43, 9, 9, 39, 9, 5, 3, 33, 27, 9, 27, 39, 3, 5, 3, 9, 141, 75, 27, 5, 53, 63, 99, 17, 57, 9, 39, 89, 33, 27, 3, 33, 45, 113, 29, 75, 9, 71, 125, 71, 149, 17, 99, 123, 3, 39, 105, 3, 27, 27, 9, 39, 163, 101, 43

Offset: 1

Author

Jianing Song, May 11 2021

Keywords

• nonn

Comments

A more intuitive version of A344141.

Every term other than the first is a member of A129771.

In A057496 it is stated that if x^n + x^3 + x^2 + x + 1 is irreducible, then so is x^n + x^3 + 1. It follows that no term can be equal to 15.

It is conjectured that no term can be of the form P_m(2^k), where P_m(x) = Product_{i>=0} (1 + x^(2^(d_i)))^(c_i) if the binary representation of m is m = Sum_{i>=0} c_i * 2^(d_i), k is an odd number. See my conjecture in A344177.

Examples

			See A344141.
		

Links

• Jianing Song, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A014580, A344141, A344186, A129771, A344177.

Programs

PARI

A344185(n) = for(k=0, 2^n-1, if(polisirreducible(Mod(Pol(binary(2^n+k)), 2)), return(k)))