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A131122 Even numbers that are not the sum of an evil prime (A027699) and an odious prime (A027697). 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 26 05:53 EDT 2022. Contains 356986 sequences. (Running on oeis4.)