A085317 - OEIS

%I #27 Jun 21 2022 14:05:38

%S 3,11,17,19,29,41,43,53,59,61,67,73,83,89,97,101,107,109,113,131,137,

%T 139,149,157,163,173,179,181,193,197,211,227,229,233,241,251,257,269,

%U 277,281,283,293,307,313,317,331,337,347,349,353,373,379,389,397,401

%N Primes which are the sum of three nonzero squares.

%C 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

%C Primes of the form a^2 + b^2 + c^2 with 1 <= a <= b <= c. - _Zak Seidov_, Nov 08 2013

%H Amiram Eldar, <a href="/A085317/b085317.txt">Table of n, a(n) for n = 1..10000</a>

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

%t 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

%t With[{nn=30},Select[Union[Total/@Tuples[Range[nn]^2,3]],PrimeQ[#]&& #<= nn^2+2&]] (* _Harvey P. Dale_, Jun 18 2022 *)

%Y Cf. A000408.

%Y Cf. A094712 (primes that are not the sum of three positive squares).

%Y Cf. A094713 (number of ways that prime(n) can be represented as a^2+b^2+c^2 with a >= b >= c > 0).

%K nonn

%O 1,1

%A _Labos Elemer_, Jul 01 2003