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

1,1

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

Links

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

Example

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

Mathematica

lst={}; lim=32; Do[n=a^2+b^2+c^2; If[n<lim^2 && PrimeQ[n], lst=Union[lst, {n}]], {a, lim}, {b, a, Sqrt[lim^2-a^2]}, {c, b, Sqrt[lim^2-a^2-b^2]}]; lst
With[{nn=30}, Select[Union[Total/@Tuples[Range[nn]^2, 3]], PrimeQ[#]&& #<= nn^2+2&]] (* Harvey P. Dale, Jun 18 2022 *)

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).

Sequence in context: A322171 A038946 A095280 * A210311 A033200 A369171

Adjacent sequences: A085314 A085315 A085316 * A085318 A085319 A085320

Keyword

nonn

Author

Labos Elemer, Jul 01 2003

Status

approved