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A344143
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Indices k such that A344141(k) and A344142(k) are not equal.
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3
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33, 34, 36, 37, 42, 49, 54, 55, 58, 59, 62, 65, 68, 71, 72, 73, 74, 76, 78, 79, 80, 82, 86, 87, 88, 89, 90, 91, 92, 94, 95, 96, 98, 100, 102, 103, 106, 107, 108, 110, 111, 113, 115, 118, 121, 124, 125, 126, 131, 132, 133, 134, 135, 137, 138, 139, 140, 141
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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.
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.
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PROG
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(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.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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