A256651 Numbers k for which both the number of evil numbers <= k and relatively prime to k, and the number of odious numbers <= k and relatively prime to k, are primes.

7, 8, 10, 11, 14, 20, 22, 24, 27, 28, 30, 39, 45, 46, 47, 48, 59, 60, 66, 81, 94, 96, 107, 118, 124, 147, 166, 167, 172, 179, 189, 192, 200, 203, 210, 214, 225, 227, 231, 247, 259, 277, 285, 296, 304, 309, 315, 323, 324, 325, 327, 334, 358, 360, 407, 412, 436

Offset: 1

Author

Vladimir Shevelev, Apr 06 2015

Keywords

• nonn
• base

Comments

For odious-evil partition of positive integers, see A000069, A001969; for odious-evil partition of relatively prime to n numbers <=n, see A230070, A230120.

Since Euler totient sequence A000010 takes only even values, then for some of them we have a representations as a sum of two primes.

Links

• Peter J. C. Moses, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000010, A000069, A001969, A230070, A230120.

Programs

PARI

is(k) = {my(c1 = 0, c2 = 0, h); for(i = 1, k, if(gcd(i, k) == 1, h = hammingweight(i) % 2; c1 += h; c2 += !h)); isprime(c1) && isprime(c2);} \\ Amiram Eldar, Nov 10 2024

Extensions

More terms from Peter J. C. Moses, Apr 06 2015