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A354572 Prime partial sums of the primes == 1 (mod 6).

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