A152715 Primes in A065049 which are not in A139370.

277, 337, 349, 373, 853, 1093, 1109, 1117, 1237, 1297, 1301, 1303, 1361, 1367, 1373, 1381, 1399, 1429, 1489, 1493, 1621, 1861, 1873, 1877, 1879, 2389, 3413, 3541, 4177, 4357, 4373, 4421, 4423, 4441, 4447, 4549, 4561, 4567, 4597, 4933, 4951, 4957, 5077, 5189, 5197, 5209, 5233, 5237

Offset: 1

Author

Vladimir Shevelev, Dec 11 2008, Dec 12 2008

Keywords

• nonn

Comments

In the notation of A139370, a prime p is in the sequence iff e(p)>o(p) and e(p)-o(p)== 4 or 5 (mod 6). [Vladimir Shevelev, Dec 12 2008]

Crossrefs

Cf. A065049, A139370.

Programs

Mathematica

aQ[n_] := PrimeQ[n] && EvenQ[Count[IntegerDigits[n, 2], 1]] == OddQ[Mod[n, 3]] && Module[{d = Reverse[IntegerDigits[n, 2]]}, Total@d[[1;; -1;; 2]] >= Total@d[[2;; -1;; 2]]]; Select[Range[5300], aQ] (* Amiram Eldar, Dec 15 2018 *)

PARI

isokp(p) = (p>2) && isprime(p) && ((hammingweight(p) % 2) != ((p % 3) % 2)); \\ A065049
isok0(n) = {my(irb = Vec(select(x->(x%2), Vecrev(binary(n)), 1))); #select(x->(x%2), irb) < #irb/2;} \\ A139370
isok(p) = isokp(p) && !isok0(p); \\ Michel Marcus, Dec 15 2018

Extensions

Missing 853 and more terms from Michel Marcus, Dec 15 2018