A094712 Primes that are not the sum of three positive squares.

2, 5, 7, 13, 23, 31, 37, 47, 71, 79, 103, 127, 151, 167, 191, 199, 223, 239, 263, 271, 311, 359, 367, 383, 431, 439, 463, 479, 487, 503, 599, 607, 631, 647, 719, 727, 743, 751, 823, 839, 863, 887, 911, 919, 967, 983, 991

Offset: 1

Author

T. D. Noe, May 21 2004

Keywords

• nonn

Comments

Except for primes 2, 5, 13 and 37, this sequence consists all primes p such that p = 7 (mod 8). The density of these primes is 0.25.

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A085317 (primes that are the sum of three positive squares).

Programs

Mathematica

lst={}; lim=32; Do[n=a^2+b^2+c^2; If[n?(AllTrue[Sqrt[#],IntegerQ]&)]==0&] (* _Harvey P. Dale, May 04 2025 *)