A380319 Smallest prime that is the sum of 2n+1 squares of consecutive odd primes, or 0 if no such prime exists.

83, 373, 1543, 2393, 4723, 10453, 0, 24953, 35323, 0, 56383, 98017, 0, 122701, 238879, 0, 263723, 318181, 0, 486617, 816547, 0, 874487, 817561, 0, 1130957, 1203343, 0, 3110867, 2451637, 1789391, 1987849, 2331379, 0, 2706679, 3124129, 0, 4260437, 4446319, 0

Offset: 1

Author

Michel Marcus, Jan 20 2025

Keywords

• nonn

Crossrefs

Cf. A001248 (primes squared), A082244 (analog for primes), A379760 (analog for cube of primes).

Formula

If n == 1 (mod 3), either a(n) = 0 or a(n) is the sum of the squares of the primes 3, 5, ..., prime(2*n+2), because p^2 == 1 (mod 3) for all primes p > 3 so the sum of 2*n+1 such primes is divisible by 3. - Pontus von Brömssen, Jan 20 2025

Extensions

Escape clause and more terms added by Pontus von Brömssen, Jan 20 2025