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A344143 Indices k such that A344141(k) and A344142(k) are not equal.

%I A344143 #19 May 11 2021 08:40:50
%S A344143 33,34,36,37,42,49,54,55,58,59,62,65,68,71,72,73,74,76,78,79,80,82,86,
%T A344143 87,88,89,90,91,92,94,95,96,98,100,102,103,106,107,108,110,111,113,
%U A344143 115,118,121,124,125,126,131,132,133,134,135,137,138,139,140,141
%N A344143 Indices k such that A344141(k) and A344142(k) are not equal.
%C A344143 A344141 and A344142 are two different methods of finding the "first irreducible GF(2)[X] polynomial of degree k". Sequence gives k such that this two methods disagree.
%C A344143 Obviously, k is a term if and only if A000120(A344141(k)) != A000120(A344142(k)).
%H A344143 Jianing Song, <a href="/A344143/b344143.txt">Table of n, a(n) for n = 1..725</a>
%e A344143 33 is a term, since lexicographically the first irreducible GF(2)[X] polynomial of degree 33 is x^33 + x^6 + x^3 + x + 1, while lexicographically the first irreducible GF(2)[X] polynomial with the lowest possible number of terms is x^33 + x^10 + 1.
%e A344143 37 is a term, since lexicographically the first irreducible GF(2)[X] polynomial of degree 37 is x^37 + x^5 + x^4 + x^3 + x^2 + x + 1, while lexicographically the first irreducible GF(2)[X] polynomial with the lowest possible number of terms is x^37 + x^6 + x^4 + x + 1.
%e A344143 54 is a term, since lexicographically the first irreducible GF(2)[X] polynomial of degree 54 is x^54 + x^6 + x^5 + x^4 + x^3 + x^2 + 1, while lexicographically the first irreducible GF(2)[X] polynomial with the lowest possible number of terms is x^54 + x^9 + 1.
%o A344143 (PARI) isA344143(n) = my(k=A344142(n)-1); while(k>=2^n, if(polisirreducible(Mod(Pol(binary(k)), 2)), return(1), k--)); 0 \\ See A344142 for its program, assuming that an irreducible polynomial of degree n with at most 5 terms exists for every n.
%Y A344143 Cf. A014580, A344141, A344142, A000120.
%K A344143 nonn
%O A344143 1,1
%A A344143 _Jianing Song_, May 10 2021