A214514 Numbers of the form p^2 + q^2 + r^2, where p, q, and r are primes.

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

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