A363074 Prime numbers that are the exact average of two consecutive odd semiprimes.

23, 29, 37, 53, 61, 67, 73, 89, 103, 113, 131, 137, 157, 173, 211, 251, 277, 293, 307, 337, 379, 409, 449, 461, 487, 491, 499, 503, 523, 569, 617, 631, 661, 683, 701, 719, 727, 751, 769, 787, 919, 941, 953, 991, 1009, 1019, 1039, 1051, 1063, 1117, 1153, 1193, 1201, 1223, 1259, 1279, 1289, 1381, 1399

Offset: 1

Author

Elmo R. Oliveira, May 20 2023

Keywords

• nonn

Examples

			23 is a term because (21 + 25)/2 = 23 is prime.
29 is a term because (25 + 33)/2 = 29 is prime.
		

Crossrefs

Cf. A000040, A046315.

Cf. A363187, A363188.

Programs

Mathematica

Select[Plus @@@ Partition[Select[Range[1, 1410, 2], PrimeOmega[#] == 2 &], 2, 1] / 2, PrimeQ] (* Amiram Eldar, May 21 2023 *)

Python

from itertools import count, islice
from sympy import factorint, isprime
def semiprime(n): return sum(e for e in factorint(n).values()) == 2
def nextoddsemiprime(n): return next(k for k in count(n+1+(n&1), 2) if semiprime(k))
def agen(): # generator of terms
    osp = [9, 15]
    while True:
        q, r = divmod(sum(osp), len(osp))
        if r == 0 and isprime(q):
            yield q
        osp = osp[1:] + [nextoddsemiprime(osp[-1])]
print(list(islice(agen(), 59))) # Michael S. Branicky, May 21 2023