OFFSET
1,1
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).
From Reinhard Zumkeller, Jul 05-12 2011, values for maximum n corrected by Antti Karttunen, May 18 2015: (Start)
a(n) = A192506(n) for n <= 36.
a(n) = A175526(n) for n <= 36.
(End)
LINKS
PROG
(PARI)
isA014580(n)=polisirreducible(Pol(binary(n))*Mod(1, 2)); \\ This function from Charles R Greathouse IV
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)));
CROSSREFS
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]).
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 03 2004
STATUS
approved