A376916 Primes that are the sum of some number of consecutive prime squares.

13, 83, 373, 653, 1543, 2393, 3271, 4519, 4723, 5381, 6701, 7591, 8069, 8219, 9439, 10453, 11719, 19541, 20269, 20477, 23599, 24821, 24953, 32939, 35323, 38219, 39631, 41539, 45319, 51031, 53549, 55721, 56179, 56383, 56599, 56909, 65419, 69389, 73331, 74441, 75997, 81299, 87589, 89459, 90199, 93581, 96661, 97847, 98017, 107741, 108827, 109849

Offset: 1

Author

Robert Israel, Oct 09 2024

Keywords

• nonn

Comments

Primes in A340771.

Examples

			a(3) = 373 is a term because 373 is prime and 373 = 3^2 + 5^2 + 7^2 + 11^2 + 13^2 where 3, 5, 6, 11 and 13 are consecutive primes.
		

Links

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

Crossrefs

Cf. A340771.

Programs

Maple

N:= 2*10^5: # for terms <= N
PS:= [0, seq(ithprime(i)^2, i=1..numtheory:-pi(floor(sqrt(N))))]:
SPS:= ListTools:-PartialSums(PS):
sort(convert(select(t -> t <= N and isprime(t), {seq(seq(SPS[t]-SPS[s], s=1..t-2), t=2..nops(SPS))}), list);