A131122 Even numbers that are not the sum of an evil prime (A027699) and an odious prime (A027697).

2, 4, 6, 8, 20, 26, 32, 38, 68, 86, 92, 98, 128, 164, 188, 278, 302, 512, 2048, 8192, 32768, 131072, 524288, 2097152, 8388608, 33554432, 134217728, 536870912

Offset: 1

Author

T. D. Noe, Jun 15 2007

Keywords

• nonn
• more

Comments

Every power of 2 with an odd exponent is a term.

Every pair of primes that sum to 4^k, with k > 1, consists of an evil prime and an odious prime. The smallest example is 16 = 3+13 = 5+11; 3 and 5 are evil, 11 and 13 are odious.

Examples

			32 is here because 32 = 3+29 = 13+19, 3 and 29 are both odious, and 13 and 19 are both evil.
		

Crossrefs

Cf. A004171 (odd powers of 2), A027697, A027699.

Programs

PARI

isok(n) = {if ((n % 2) == 0, forprime(p=3, n, if ((norml2(binary(p))%2==1) && (isprime(q=n-p)) && (!bittest(norml2(binary(q)), 0)), return (0));); return (1);); return(0);}
lista(nn) = forstep(n=2, nn, 2, if (isok(n), print1(n, ", "))); \\ Michel Marcus, Oct 14 2018

Extensions

a(23)-a(28) from Michel Marcus, Oct 14 2018