A363187 Prime numbers that are the average of three consecutive odd semiprimes.

31, 41, 59, 83, 107, 139, 163, 191, 197, 281, 311, 383, 397, 443, 521, 673, 677, 757, 821, 887, 997, 1061, 1109, 1151, 1171, 1229, 1237, 1373, 1423, 1453, 1619, 1823, 1889, 1931, 2053, 2141, 2203, 2221, 2309, 2339, 2437, 2473, 2477, 2749, 2801, 2837, 2953, 3019, 3119, 3163, 3209, 3257, 3347

Offset

1,1

Links

Gabriel Whigham, Table of n, a(n) for n = 1..10000

Example

31 is a term because (25 + 33 + 35)/3 = 31 is prime.
41 is a term because (35 + 39 + 49)/3 = 41 is prime.

Maple

OP:= select(isprime, [seq(i, i=3..10000, 2)]):
OSP:= sort(select(`<=`, [seq(seq(OP[i]*OP[j], j=1..i), i=1..nops(OP))], 3*OP[-1])):
SA:= [seq(add(OSP[i+j], j=0..2)/3, i=1..nops(OSP)-2)]:
select(t -> t::integer and isprime(t), SA); # Robert Israel, May 22 2023

Mathematica

Select[Plus @@@ Partition[Select[Range[1, 3400, 2], PrimeOmega[#] == 2 &], 3, 1] / 3, 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, 21]
    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(), 53))) # Michael S. Branicky, May 21 2023

Crossrefs

Cf. A000040, A046315.

Cf. A363074, A363188.

Sequence in context: A238397 A087054 A245650 * A098711 A087053 A159045

Adjacent sequences: A363184 A363185 A363186 * A363188 A363189 A363190

Keyword

nonn

Author

Elmo R. Oliveira, May 20 2023

Status

approved