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A094712 Primes that are not the sum of three positive squares. 3
2, 5, 7, 13, 23, 31, 37, 47, 71, 79, 103, 127, 151, 167, 191, 199, 223, 239, 263, 271, 311, 359, 367, 383, 431, 439, 463, 479, 487, 503, 599, 607, 631, 647, 719, 727, 743, 751, 823, 839, 863, 887, 911, 919, 967, 983, 991 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..10000

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

CROSSREFS

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

Sequence in context: A045355 A252281 A165319 * A095281 A106889 A155028

Adjacent sequences:  A094709 A094710 A094711 * A094713 A094714 A094715

KEYWORD

nonn

AUTHOR

T. D. Noe, May 21 2004

STATUS

approved

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Last modified April 25 21:06 EDT 2019. Contains 322461 sequences. (Running on oeis4.)