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A354573 Prime partial sums of the primes == 5 (mod 6).

%I A354573 #14 Aug 23 2022 17:49:03
%S A354573 5,173,439,1117,1433,2633,3643,6173,11489,22727,25867,36523,51341,
%T A354573 71707,80347,89413,98947,102203,119869,135209,155653,173087,182233,
%U A354573 196387,226063,298031,353921,367219,460127,483179,498859,547387,555683,572581,826201,932801,988453,1057741,1203421,1253999
%N A354573 Prime partial sums of the primes == 5 (mod 6).
%C A354573 Primes in A038361.
%H A354573 Robert Israel, <a href="/A354573/b354573.txt">Table of n, a(n) for n = 1..10000</a>
%e A354573 a(2) = 173 is a term because 173 = A038361(7) = 5+11+17+23+29+41+47 and is prime.
%p A354573 R:= NULL: count:= 0: t:= 0:
%p A354573 for p from 5 by 6 while count < 100 do
%p A354573   if isprime(p) then
%p A354573     t:= t+p;
%p A354573     if isprime(t) then R:= R, t; count:= count+1 fi
%p A354573   fi
%p A354573 od:
%p A354573 R;
%t A354573 Select[Accumulate[Select[Prime[Range[1000]], Mod[#, 6] == 5 &]], PrimeQ] (* _Amiram Eldar_, Aug 19 2022 *)
%Y A354573 Cf. A038361, A354572.
%K A354573 nonn
%O A354573 1,1
%A A354573 _J. M. Bergot_ and _Robert Israel_, Aug 18 2022