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

1,1

Comments

Primes in A340771.

Links

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

Example

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.

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);

Crossrefs

Cf. A340771.

Sequence in context: A101102 A213572 A142085 * A163688 A274398 A301953

Adjacent sequences: A376913 A376914 A376915 * A376917 A376918 A376919

Keyword

nonn

Author

Robert Israel, Oct 09 2024

Status

approved