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Prime partial sums of the primes == 1 (mod 6).
2

%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