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

1,1

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

Prog

(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

Crossrefs

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

Sequence in context: A096677 A120192 A333490 * A093678 A188052 A266727

Adjacent sequences: A256648 A256649 A256650 * A256652 A256653 A256654

Keyword

nonn,base

Author

Vladimir Shevelev, Apr 06 2015

Extensions

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

Status

approved