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

Offset: 1

Author

M. F. Hasler, May 18 2009

Keywords

• nonn

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

Crossrefs

Cf. A098562, A133547.

Programs

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 *)

PARI

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

Formula

Equals A000040 intersect A133547.