A085317 Primes which are the sum of three nonzero squares.

3, 11, 17, 19, 29, 41, 43, 53, 59, 61, 67, 73, 83, 89, 97, 101, 107, 109, 113, 131, 137, 139, 149, 157, 163, 173, 179, 181, 193, 197, 211, 227, 229, 233, 241, 251, 257, 269, 277, 281, 283, 293, 307, 313, 317, 331, 337, 347, 349, 353, 373, 379, 389, 397, 401

Offset: 1

Author

Labos Elemer, Jul 01 2003

Keywords

• nonn

Comments

This sequence consists of the primes p (not 5, 13, or 37) such that p == 1, 3 or 5 (mod 8). The density of these primes is 0.75. - T. D. Noe, May 21 2004

Primes of the form a^2 + b^2 + c^2 with 1 <= a <= b <= c. - Zak Seidov, Nov 08 2013

Examples

			101 is a term since 101 = 64 + 36 + 1 = 8^2 + 6^2 + 1^2.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000408.

Cf. A094712 (primes that are not the sum of three positive squares).

Cf. A094713 (number of ways that prime(n) can be represented as a^2+b^2+c^2 with a >= b >= c > 0).

Programs

Mathematica

lst={}; lim=32; Do[n=a^2+b^2+c^2; If[nHarvey P. Dale, Jun 18 2022 *)