

A085317


Primes which are the sum of three squares.


8



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
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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

Table of n, a(n) for n=1..55.


EXAMPLE

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^2a^2]}, {c, b, Sqrt[lim^2a^2b^2]}]; lst


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: A154497 A038946 A095280 * A210311 A033200 A191375
Adjacent sequences: A085314 A085315 A085316 * A085318 A085319 A085320


KEYWORD

nonn


AUTHOR

Labos Elemer, Jul 01 2003


STATUS

approved



