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

%I #14 Feb 14 2021 08:04:28

%S 1,11,19,29,37,73,97,155,163,175,191,257,295,313,325,341,365,389,391,

%T 409,415,461,491,497,515,599,697,715,757,761,767,775,785,793,857,875,

%U 895,899,905,919,1099,1109,1117,1139,1151,1163,1225,1271,1279,1295,1309

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

%H Harvey P. Dale, <a href="/A277123/b277123.txt">Table of n, a(n) for n = 1..1000</a>

%t Position[Accumulate[Prime[Range[2000]]^2]+1,_?PrimeQ]//Flatten (* _Harvey P. Dale_, Sep 07 2019 *)

%o (Python)

%o import sympy

%o sum = p = 1

%o for n in range(1,3001):

%o while not sympy.isprime(p): p+=1 # find the n'th prime

%o sum += p*p

%o p+=1

%o if sympy.isprime(sum): print str(n)+',',

%o (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 Cf. A000040, A013916, A089228, A131694, A159260.

%K nonn

%O 1,2

%A _Alex Ratushnyak_, Sep 30 2016