A160359 - OEIS

A160359

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

83, 373, 2393, 4723, 56383, 122701, 1789391, 1987849, 2706679, 7287991, 27833021, 41765519, 43570537, 55600477, 62283451, 67053359, 104720809, 122353547, 204330311, 347756707, 450504547, 540649093, 677774533, 715849843, 839886301

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OFFSET

1,1

COMMENTS

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.

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

Equals A000040 intersect A133547.

MAPLE

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

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

select(isprime, S); # Robert Israel, May 13 2024

MATHEMATICA

Select[Accumulate[Prime[Range[2, 400]]^2], PrimeQ] (* Harvey P. Dale, Jul 17 2021 *)

PROG

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