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Numbers n such that x^n * (x+1)^(n-1) + 1 is irreducible over GF(2).
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%I #31 Dec 01 2022 17:20:53

%S 1,2,3,4,5,8,21,32,33,36,53,64,85,89,148,312,404,3080,8380,11684,

%T 16384,18089,21096,53492,78484,192248

%N Numbers n such that x^n * (x+1)^(n-1) + 1 is irreducible over GF(2).

%C Any subsequent terms are > 2 * 10^5. - _Lucas A. Brown_, Dec 01 2022

%o (Sage)

%o P.<x> = GF(2)[]

%o for n in range(1, 10^5):

%o if (x^n * (x+1)^(n-1) + 1).is_irreducible():

%o print(n)

%o (PARI) isok(n) = polisirreducible(Mod(1, 2)*x^n * (x+1)^(n-1) + 1); \\ _Michel Marcus_, Mar 03 2016

%Y Cf. A162570 (corresponding to powers of 2 in this sequence).

%K nonn,more,hard

%O 1,2

%A _Joerg Arndt_, Mar 02 2016

%E a(26) from _Lucas A. Brown_, Dec 01 2022