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

1,1

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Primes in A062198. Cf. A001358.

Sequence in context: A046120 A063644 A156782 * A092600 A106124 A062679

Adjacent sequences: A347363 A347364 A347365 * A347367 A347368 A347369

Keyword

nonn

Author

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

Status

approved