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A057489 Numbers n > 13 such that x^n + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1 is irreducible over GF(2). 0

%I #18 Nov 29 2022 08:38:25

%S 15,21,25,42,43,48,60,97,106,133,147,148,178,201,252,253,327,513,570,

%T 732,763,1108,1342,1572,2175,2407,2605,2850,3930,4627,6181,6312,7048,

%U 7596,8995,9250,9873,11841,12471,13927,20658,20965,33957,72373,91992,156657

%N Numbers n > 13 such that x^n + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1 is irreducible over GF(2).

%C No terms == 2 mod 3 or == 4 mod 5. - _Robert Israel_, Feb 22 2017

%p Q:= add(x^i,i=0..13):

%p select(t -> Irreduc(x^t+Q) mod 2, [$14..1000]); # _Robert Israel_, Feb 22 2017

%o (PARI) isok(n) = (n>13) && polisirreducible(Mod(1,2)*(x^n+sum(k=0, 13, x^k))); \\ _Michel Marcus_, Feb 23 2017

%K nonn

%O 1,1

%A _Robert G. Wilson v_, Sep 28 2000

%E a(22)-a(24) from _Robert Israel_, Feb 22 2017

%E a(25)-a(32) from _Jinyuan Wang_, Apr 15 2020

%E a(33)-a(47) from _Lucas A. Brown_, Nov 29 2022

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Last modified July 23 21:46 EDT 2024. Contains 374575 sequences. (Running on oeis4.)