%I #25 Jun 25 2022 12:53:54

%S 13,20477,75997,239087,2210983,3579761,29194283,40002073,45448471,

%T 55600481,77290091,108095623,114986483,155637463,226226771,302920139,

%U 324657881,519681709,551321299,618359839,797005427,944007487,1039681147,1124764853,1923614047,2135308631

%N Primes that are the sum of the squares of the first k primes for some k.

%C These are the primes arising in A098561.

%H K. D. Bajpai, <a href="/A098562/b098562.txt">Table of n, a(n) for n = 1..15000</a>

%e From _K. D. Bajpai_, Dec 15 2014: (Start)

%e 13 is in the sequence because the sum of the squares of the first 2 primes is 2^2 + 3^2 = 4 + 9 = 13, which is prime.

%e 20477 is in the sequence because the sum of the squares of the first 18 primes is 2^2 + 3^2 + 5^2 + ... + 59^2 + 61^2 = 4 + 9 + 25 + ... + 3481 + 3721 = 20477, which is prime.

%e (End)

%t Select[Table[Sum[Prime[k]^2, {k, 1, n}], {n, 1000}], PrimeQ] (* _K. D. Bajpai_, Dec 15 2014 *)

%o (PARI) s=0; forprime(p=2, 1e6, t=s+=p^2; if(isprime(t), print1(t,", "))) \\ _K. D. Bajpai_, Dec 15 2014

%Y Cf. A098561 (corresponding n), A024450 (sum of squares of primes), A066525 (sums of cubes of primes), A013918 (sums of primes).

%Y Cf. A000040, A006567. - _Jonathan Vos Post_, Aug 13 2009

%K nonn

%O 1,1

%A _Rick L. Shepherd_, Sep 14 2004

%E a(24)-a(26) from _K. D. Bajpai_, Dec 15 2014

%E a(42) in b-file corrected by _Andrew Howroyd_, Feb 28 2018