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A346706 Lesser members of twin primes which are the sum of the first k primes for some number k.

%I A346706 #35 Sep 26 2021 16:08:03
%S A346706 5,17,41,197,281,38921,121631,325019,642869,681257,1005551,1086557,
%T A346706 2327399,4975457,7584569,7819787,8130767,8522159,14848187,17769377,
%U A346706 18615677,19949537,20144051,21171191,24845207,33669047,35166449,56039957,73479947,82366769,92731367
%N A346706 Lesser members of twin primes which are the sum of the first k primes for some number k.
%H A346706 Sebastian Sargenti, <a href="/A346706/b346706.txt">Table of n, a(n) for n = 1..128</a>
%e A346706 5 = 2+3; 5 is a twin prime with 7.
%e A346706 17 = 2+3+5+7; 17 is a twin prime with 19.
%e A346706 41 = 2+3+5+7+11+13; 41 is a twin prime with 43.
%e A346706 197 = 2+3+5+7+11+13+17+19+23+29+31+37; 197 is a twin prime with 199.
%t A346706 Select[Accumulate @ Select[Range[45000], PrimeQ], PrimeQ[#] && PrimeQ[# + 2] &] (* _Amiram Eldar_, Aug 01 2021 *)
%o A346706 (Python)
%o A346706 from itertools import accumulate
%o A346706 from sympy import isprime, primerange
%o A346706 list(filter(lambda p: isprime(p) and isprime(p+2), accumulate(primerange(2, 10000)))) # _David Radcliffe_, Aug 01 2021
%o A346706 (PARI) lista(nn) = {my(s=0); for (n=1, nn, s += prime(n); if (isprime(s) && isprime(s+2), print1(s, ", ")););} \\ _Michel Marcus_, Aug 21 2021
%Y A346706 Cf. A000040, A007504.
%Y A346706 Intersection of A001359 and A013918.
%K A346706 nonn
%O A346706 1,1
%A A346706 _Sebastian Sargenti_, Jul 29 2021
%E A346706 a(13)-a(31) from _Jon E. Schoenfield_, Jul 29 2021