The On-Line Encyclopedia of Integer Sequences (OEIS)

A152715 revision #8

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

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]

LINKS

Table of n, a(n) for n=1..48.

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 *)

PROG

(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

CROSSREFS

Cf. A065049, A139370.

Sequence in context: A045022 A108253 A108255 * A139654 A046504 A142542

Adjacent sequences: A152712 A152713 A152714 * A152716 A152717 A152718

KEYWORD

nonn

AUTHOR

Vladimir Shevelev, Dec 11 2008, Dec 12 2008

EXTENSIONS

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

STATUS

approved