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
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 IntSeq-library)
CROSSREFS
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.
KEYWORD
nonn
AUTHOR
Antti Karttunen, May 07 2015
STATUS
approved