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A277123 Numbers k such that 1 + Sum_{j=1..k} prime(j)^2 is prime.

%I A277123 #17 May 19 2025 23:44:59
%S A277123 1,11,19,29,37,73,97,155,163,175,191,257,295,313,325,341,365,389,391,
%T A277123 409,415,461,491,497,515,599,697,715,757,761,767,775,785,793,857,875,
%U A277123 895,899,905,919,1099,1109,1117,1139,1151,1163,1225,1271,1279,1295,1309
%N A277123 Numbers k such that 1 + Sum_{j=1..k} prime(j)^2 is prime.
%H A277123 Harvey P. Dale, <a href="/A277123/b277123.txt">Table of n, a(n) for n = 1..1000</a>
%t A277123 Position[Accumulate[Prime[Range[2000]]^2]+1,_?PrimeQ]//Flatten (* _Harvey P. Dale_, Sep 07 2019 *)
%o A277123 (Python)
%o A277123 import sympy
%o A277123 sum = p = 1
%o A277123 for n in range(1,3001):
%o A277123   while not sympy.isprime(p):  p+=1    # find the n'th prime
%o A277123   sum += p*p
%o A277123   p+=1
%o A277123   if sympy.isprime(sum):  print(n, end=', ')
%o A277123 (PARI) lista(nn) = for(n=1, nn, if(isprime(1+sum(i=1, n, prime(i)^2)), print1(n, ", "))); \\ _Altug Alkan_, Oct 01 2016
%Y A277123 Cf. A000040, A013916, A089228, A131694, A159260.
%K A277123 nonn
%O A277123 1,2
%A A277123 _Alex Ratushnyak_, Sep 30 2016