A347366 Primes that are partial sums of the semiprimes.

19, 29, 43, 79, 101, 331, 647, 709, 2039, 4723, 5261, 5827, 10271, 11057, 12163, 12743, 20183, 22039, 22807, 25999, 30319, 33563, 44777, 45319, 56843, 60623, 61927, 73583, 83077, 108013, 133447, 142183, 159541, 182659, 191833, 204803, 214463, 215689, 248789, 266239, 292573, 302593, 314339, 318823

Offset: 1

Author

J. M. Bergot and Robert Israel, Aug 29 2021

Keywords

• nonn

Examples

			a(3) = 43 is a term because 43 = A062198(5) is prime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Primes in A062198. Cf. A001358.

Programs

Maple

SP:= select(t -> numtheory:-bigomega(t) = 2, [$2..10000]):
PSSP:= ListTools:-PartialSums(SP):
select(isprime,PSSP);

Mathematica

Select[Accumulate @ Select[Range[1500], PrimeOmega[#] == 2 &], PrimeQ] (* Amiram Eldar, Aug 29 2021 *)

Python

from sympy import factorint, isprime
def aupto(limit):
    alst, k, s = [], 1, 0
    for k in range(1, limit+1):
        if sum(factorint(k).values()) == 2:
            s += k
            if s > limit: break
            if isprime(s): alst.append(s)
    return alst
print(aupto(320000)) # Michael S. Branicky, Aug 29 2021