A214514 -id:A214514 - cp's OEIS frontend

A214515 Numbers of the form p^2 + q^2 + r^2 + s^2, where p, q, r, and s are primes.

16, 21, 26, 31, 36, 37, 42, 47, 52, 58, 61, 63, 66, 68, 71, 76, 79, 82, 84, 87, 92, 100, 103, 106, 108, 111, 116, 124, 127, 132, 133, 138, 143, 148, 151, 154, 156, 159, 164, 172, 175, 178, 180, 181, 183, 186, 188, 191, 196, 199, 202, 204, 207, 212, 220, 223

Offset: 1

T. D. Noe, Jul 29 2012

nonn

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

Cf. A045636 (two primes), A214514 (three primes).

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

A302359 Numbers that are the sum of 3 squares > 1.

Original entry on oeis.org

12, 17, 22, 24, 27, 29, 33, 34, 36, 38, 41, 43, 44, 45, 48, 49, 50, 54, 56, 57, 59, 61, 62, 65, 66, 67, 68, 69, 70, 72, 74, 75, 76, 77, 78, 81, 82, 83, 84, 86, 88, 89, 90, 93, 94, 96, 97, 98, 99, 101, 102, 104, 105, 106, 107, 108, 109, 110, 113, 114, 115, 116, 117, 118, 120, 121, 122, 123, 125, 126, 129

Offset: 1

Ilya Gutkovskiy, Apr 06 2018

nonn

			33 is in the sequence because 33 = 2^2 + 2^2 + 5^2.

Michael S. Branicky, Table of n, a(n) for n = 1..10000
Index entries for sequences related to sums of squares

Cf. A000378, A000408, A085989, A214514, A281155.

max = 130; f[x_] := Sum[x^(k^2), {k, 2, 20}]^3; Exponent[#, x] & /@ List @@ Normal[Series[f[x], {x, 0, max}]]
With[{nn=15},Select[Union[Total/@Tuples[Range[2,nn]^2,3]],#<=nn^2+8&]] (* Harvey P. Dale, Jul 05 2021 *)

from itertools import count, takewhile, combinations_with_replacement as mc
def aupto(N):
    sqrs = list(takewhile(lambda x: x<=N, (i**2 for i in count(2))))
    sum3 = set(sum(c) for c in mc(sqrs, 3) if sum(c) <= N)
    return sorted(sum3)
print(aupto(129)) # Michael S. Branicky, Dec 17 2021

cp's OEIS Frontend

A214515 Numbers of the form p^2 + q^2 + r^2 + s^2, where p, q, r, and s are primes.

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