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A257688
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After 1, all numbers that are either primes in Z or whose binary representation encodes a polynomial irreducible over GF(2).
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9
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1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 25, 29, 31, 37, 41, 43, 47, 53, 55, 59, 61, 67, 71, 73, 79, 83, 87, 89, 91, 97, 101, 103, 107, 109, 113, 115, 117, 127, 131, 137, 139, 143, 145, 149, 151, 157, 163, 167, 171, 173, 179, 181, 185, 191, 193, 197, 199, 203, 211, 213, 223, 227, 229, 233, 239, 241, 247, 251, 253, 257, 263, 269
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OFFSET
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1,2
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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).
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LINKS
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PROG
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(PARI)
isA257688(n) = ((1 == n) || isprime(n) || isA014580(n));
n = 0; i = 0; while(i < 10000, n++; if(isA257688(n), i++; write("b257688.txt", i, " ", n)));
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CROSSREFS
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Complement of A091212 (Numbers that are composite in Z and reducible in ring GF(2)[X]).
After the initial 1, a subsequence of A206074 (n-th irreducible polynomial over Q (with coefficients 0 or 1) evaluated at x=2), from which this differs for the first time at n=23, where a(23)=71, while A206074(22) = 69, the first term missing from here.
Differs from A186891 for the first time at n=22, where a(22) = 67, while A186891(22) = 65.
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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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