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A094712 Primes that are not the sum of three positive squares. 3


%S 2,5,7,13,23,31,37,47,71,79,103,127,151,167,191,199,223,239,263,271,

%T 311,359,367,383,431,439,463,479,487,503,599,607,631,647,719,727,743,

%U 751,823,839,863,887,911,919,967,983,991

%N Primes that are not the sum of three positive squares.

%C Except for primes 2, 5, 13 and 37, this sequence consists all primes p such that p = 7 (mod 8). The density of these primes is 0.25.

%H Chai Wah Wu, <a href="/A094712/b094712.txt">Table of n, a(n) for n = 1..10000</a>

%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]}]; Complement[Prime[Range[PrimePi[lst[[ -1]]]]], lst]

%Y Cf. A085317 (primes that are the sum of three positive squares).

%K nonn

%O 1,1

%A _T. D. Noe_, May 21 2004

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Last modified February 4 02:26 EST 2023. Contains 360045 sequences. (Running on oeis4.)