%I #14 May 13 2024 15:36:23

%S 83,373,2393,4723,56383,122701,1789391,1987849,2706679,7287991,

%T 27833021,41765519,43570537,55600477,62283451,67053359,104720809,

%U 122353547,204330311,347756707,450504547,540649093,677774533,715849843,839886301

%N Primes that are partial sums of squares of the odd primes.

%C There is necessarily an odd number of terms in the sum a(n) = 3^2+5^2+...+p(k)^2, i.e. the index k=A160358(n)+1 of the last prime in this sum is even.

%H Robert Israel, <a href="/A160359/b160359.txt">Table of n, a(n) for n = 1..10000</a>

%F Equals A000040 intersect A133547.

%p P:= select(isprime,[seq(i,i=3..10000,2)]):

%p S:= ListTools:-PartialSums(map(`^`,P,2)):

%p select(isprime,S); # _Robert Israel_, May 13 2024

%t Select[Accumulate[Prime[Range[2,400]]^2],PrimeQ] (* _Harvey P. Dale_, Jul 17 2021 *)

%o (PARI) s=0; forprime( p=3,9999, isprime(s+=p^2) & print1(s","))

%Y Cf. A098562, A133547.

%K nonn

%O 1,1

%A _M. F. Hasler_, May 18 2009