login
A085317
Primes which are the sum of three nonzero squares.
16
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
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
KEYWORD
nonn
AUTHOR
Labos Elemer, Jul 01 2003
STATUS
approved