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

1,1

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.

Links

Table of n, a(n) for n=1..28.

Example

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

Prog

(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

Crossrefs

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

Sequence in context: A251853 A061651 A350538 * A335209 A119261 A062285

Adjacent sequences: A131119 A131120 A131121 * A131123 A131124 A131125

Keyword

nonn,more

Author

T. D. Noe, Jun 15 2007

Extensions

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

Status

approved