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A214514 Numbers of the form p^2 + q^2 + r^2, where p, q, and r are primes. 3
12, 17, 22, 27, 33, 38, 43, 54, 57, 59, 62, 67, 75, 78, 83, 99, 102, 107, 123, 129, 134, 139, 147, 150, 155, 171, 174, 177, 179, 182, 187, 195, 198, 203, 219, 222, 227, 243, 246, 251, 267, 291, 294, 297, 299, 302, 307, 315, 318, 323, 339, 342, 347, 363, 369 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000

MATHEMATICA

nn = 10^3; ps = Prime[Range[PrimePi[Sqrt[nn]]]]; t = Flatten[Table[ps[[i]]^2 + ps[[j]]^2 + ps[[k]]^2, {i, Length[ps]}, {j, i, Length[ps]}, {k, j, Length[ps]}]]; t = Select[t, # <= nn &]; Union[t]

PROG

(Python)

from sympy import primerange as primes

from itertools import takewhile, combinations_with_replacement as mc

def aupto(N):

    psqs = list(takewhile(lambda x: x<=N, (p**2 for p in primes(1, N+1))))

    sum3 = set(sum(c) for c in mc(psqs, 3) if sum(c) <= N)

    return sorted(sum3)

print(aupto(369)) # Michael S. Branicky, Dec 17 2021

CROSSREFS

Cf. A045636 (two primes), A214515 (four primes).

Sequence in context: A154488 A336890 A302359 * A188004 A045699 A155096

Adjacent sequences:  A214511 A214512 A214513 * A214515 A214516 A214517

KEYWORD

nonn

AUTHOR

T. D. Noe, Jul 29 2012

STATUS

approved

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Last modified July 2 08:20 EDT 2022. Contains 354985 sequences. (Running on oeis4.)