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A214514
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Numbers of the form p^2 + q^2 + r^2, where p, q, and r are primes.
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3
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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
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listen;
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OFFSET
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1,1
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..10000
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MATHEMATICA
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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]
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PROG
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(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
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CROSSREFS
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Cf. A045636 (two primes), A214515 (four primes).
Sequence in context: A154488 A336890 A302359 * A188004 A045699 A155096
Adjacent sequences: A214511 A214512 A214513 * A214515 A214516 A214517
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe, Jul 29 2012
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STATUS
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approved
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