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

1,1

Links

Table of n, a(n) for n=1..59.

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A000040, A046315.

Cf. A363187, A363188.

Sequence in context: A353286 A101784 A101802 * A156983 A230456 A174196

Adjacent sequences: A363071 A363072 A363073 * A363075 A363076 A363077

Keyword

nonn

Author

Elmo R. Oliveira, May 20 2023

Status

approved