%I #17 Sep 05 2022 09:10:47
%S 7,107,211,739,1657,2953,4091,20479,23459,33713,35671,46133,60527,
%T 63127,77237,80209,86399,106277,127997,139871,178757,183361,197569,
%U 238853,255239,272171,353611,367019,394759,416089,460189,475421,625199,652499,808111,860393,903871,925979,959603,1005217
%N Prime partial sums of the primes == 1 (mod 6).
%C Primes in A038349.
%H Robert Israel, <a href="/A354572/b354572.txt">Table of n, a(n) for n = 1..10000</a>
%e a(3) = 211 is a term because 211 = A037349(7) = 7+13+19+31+37+43+61 and is prime.
%p R:= NULL: count:= 0: t:= 0:
%p for p from 1 by 6 while count < 100 do
%p if isprime(p) then
%p t:= t+p;
%p if isprime(t) then R:= R, t; count:= count+1 fi
%p fi
%p od:
%p R;
%t Select[Accumulate[Select[Prime[Range[1000]], Mod[#, 6] == 1 &]], PrimeQ] (* _Amiram Eldar_, Aug 18 2022 *)
%Y Cf. A038349, A354573.
%K nonn
%O 1,1
%A _J. M. Bergot_ and _Robert Israel_, Aug 18 2022