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A091212
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Composite numbers whose binary representation encodes a polynomial reducible over GF(2).
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13
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4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 88, 90, 92, 93, 94, 95, 96, 98, 99
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OFFSET
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1,1
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COMMENTS
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"Encoded in binary representation" means that a polynomial a(n)*X^n+...+a(0)*X^0 over GF(2) is represented by the binary number a(n)*2^n+...+a(0)*2^0 in Z (where each coefficient a(k) = 0 or 1).
(End)
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LINKS
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FORMULA
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PROG
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(PARI)
isA091212(n) = ((n > 1) && !isprime(n) && !isA014580(n));
n = 0; i = 0; while(n < 2^16, n++; if(isA091212(n), i++; write("b091212.txt", i, " ", n)));
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CROSSREFS
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Cf. A257688 (complement, either 1, irreducible in GF(2)[X] or prime), A091206 (prime and irreducible), A091209 (prime and reducible), A091214 (nonprime and irreducible).
Differs from both A175526 and A192506 for the first time at n=37, where a(37) = 56, while A175526(37) = A192506(37) = 55, a term missing from here (as 55 encodes a polynomial which is irreducible in GF(2)[X]).
Differs from its subsequence A205783(n+1) for the first time at n=47, where a(47) = 69, while 69 is missing from A205783.
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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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