

A257688


After 1, all numbers that are either primes in Z or whose binary representation encodes a polynomial irreducible over GF(2).


9



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

1,2


COMMENTS

"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).


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000
Index entries for sequences related to polynomials over GF(2)


PROG

(PARI)
isA014580(n) = polisirreducible(Pol(binary(n))*Mod(1, 2)); \\ From Charles R Greathouse IV
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)));
(Scheme, with Antti Karttunen's IntSeqlibrary)
(define A257688 (MATCHINGPOS 1 1 (lambda (n) (or (= 1 n) (= 1 (A091225 n)) (= 1 (A010051 n))))))


CROSSREFS

Union of A008578 and A014580.
Complement of A091212 (Numbers that are composite in Z and reducible in ring GF(2)[X]).
After the initial 1, a subsequence of A206074 (nth 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.
Differs from A257689 and A257691 for the first time at n=19, where a(19) = 55, while 55 is missing from both A257689 and A257691.
Sequence in context: A186891 A206074 A325559 * A257689 A257691 A164574
Adjacent sequences: A257685 A257686 A257687 * A257689 A257690 A257691


KEYWORD

nonn


AUTHOR

Antti Karttunen, May 07 2015


STATUS

approved



