This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A335329 #33 Jul 19 2024 14:58:26
%S A335329 29,61,197,11789,7379689,161409881,14881142931617,34041319775377
%N A335329 Primes p of the form 4k+1 such that the sum up to p of the primes of the same form is a square.
%e A335329 5+13+17+29 = 64 = 8^2.
%e A335329 5+...+161409881 = 354203842652416 = 18820304^2.
%t A335329 s=0; Select[Prime@ Range[10^9], Mod[#,4]==1 && IntegerQ@ Sqrt[s+=#] &] (* _Robert Price_, Sep 10 2020 *)
%t A335329 Module[{nn=74*10^5,k,a},k=Select[Prime[Range[nn]],Mod[#-1,4]==0&];a=Accumulate[ k];Select[ Thread[ {k,a}],IntegerQ[Sqrt[#[[2]]]]&]][[;;,1]] (* The program generates the first five terms of the sequence. *) (* _Harvey P. Dale_, Jul 19 2024 *)
%o A335329 (UBASIC)
%o A335329 10 'S1=sum of primes 4k+1, S1=sum of primes 4k+1
%o A335329 20 'is S1 a square?
%o A335329 30 S1=0:P=2:PM=2^32-10:K=1
%o A335329 40 P=nxtprm(P):K=K+1:if P>PM then end
%o A335329 50 if P@4=3 then goto 40
%o A335329 60 S1=S1+P:SS1=isqrt(S1)
%o A335329 70 if SS1*SS1=S1 then print K;P;S1;SS1;1
%o A335329 80 goto 40
%o A335329 (PARI) s=0;forprime(p=5,10^9,if(p%4==1,s+=p;if(issquare(s),print1(p,", ")))) \\ _Hugo Pfoertner_, Jun 02 2020
%Y A335329 Cf. A033998.
%K A335329 nonn,more
%O A335329 1,1
%A A335329 _Carlos Rivera_, Jun 01 2020
%E A335329 a(7) and a(8) from _Martin Ehrenstein_ using Kim Walisch's primesieve, Jan 09 2021