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A347366 Primes that are partial sums of the semiprimes. 1
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 (list; graph; refs; listen; history; text; internal format)
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:  A347361 A347364 A347365 * A347367 A347368 A347369

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified December 4 10:59 EST 2021. Contains 349486 sequences. (Running on oeis4.)