

A085317


Primes which are the sum of three nonzero squares.


10



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



