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A347366 Primes that are partial sums of the semiprimes.

%I A347366 #12 Aug 30 2021 13:42:13
%S A347366 19,29,43,79,101,331,647,709,2039,4723,5261,5827,10271,11057,12163,
%T A347366 12743,20183,22039,22807,25999,30319,33563,44777,45319,56843,60623,
%U A347366 61927,73583,83077,108013,133447,142183,159541,182659,191833,204803,214463,215689,248789,266239,292573,302593,314339,318823
%N A347366 Primes that are partial sums of the semiprimes.
%H A347366 Robert Israel, <a href="/A347366/b347366.txt">Table of n, a(n) for n = 1..10000</a>
%e A347366 a(3) = 43 is a term because 43 = A062198(5) is prime.
%p A347366 SP:= select(t -> numtheory:-bigomega(t) = 2, [$2..10000]):
%p A347366 PSSP:= ListTools:-PartialSums(SP):
%p A347366 select(isprime,PSSP);
%t A347366 Select[Accumulate @ Select[Range[1500], PrimeOmega[#] == 2 &], PrimeQ] (* _Amiram Eldar_, Aug 29 2021 *)
%o A347366 (Python)
%o A347366 from sympy import factorint, isprime
%o A347366 def aupto(limit):
%o A347366     alst, k, s = [], 1, 0
%o A347366     for k in range(1, limit+1):
%o A347366         if sum(factorint(k).values()) == 2:
%o A347366             s += k
%o A347366             if s > limit: break
%o A347366             if isprime(s): alst.append(s)
%o A347366     return alst
%o A347366 print(aupto(320000)) # _Michael S. Branicky_, Aug 29 2021
%Y A347366 Primes in A062198.  Cf. A001358.
%K A347366 nonn
%O A347366 1,1
%A A347366 _J. M. Bergot_ and _Robert Israel_, Aug 29 2021