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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 (list; graph; refs; listen; history; text; internal format)
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^2-a^2]}, {c, b, Sqrt[lim^2-a^2-b^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

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Last modified December 5 21:40 EST 2016. Contains 278771 sequences.