A389640 Numbers k such that 2*k can be represented as the sum of four distinct squares of primes.

102, 126, 162, 174, 182, 186, 222, 234, 242, 246, 258, 266, 270, 278, 282, 294, 302, 306, 314, 330, 338, 342, 350, 354, 362, 366, 378, 386, 390, 398, 410, 414, 422, 426, 434, 438, 446, 462, 470, 474, 482, 494, 498, 506, 510, 518, 522, 530, 534, 542, 554, 558, 570

Offset

1,1

Comments

The case of not necessarily distinct squares is in A389638 and A389639.

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Example

k = 102 ->  204 = 3^2 + 5^2 +  7^2 + 11^2.
k = 222 ->  444 = 3^2 + 5^2 +  7^2 + 19^2 = 3^2 +  5^2 + 11^2 + 17^2.
k = 518 -> 1036 = 5^2 + 7^2 + 11^2 + 29^2 = 5^2 + 11^2 + 19^2 + 23^2 = 7^2 + 13^2 + 17^2 + 23^2.

Mathematica

A389640list[pmax_] := With[{ps = Prime[Range[pmax + 1]]^2}, Select[Union[Flatten[Table[ps[[i]] + ps[[j]] + ps[[k]] + ps[[l]], {i, pmax}, {j, i + 1, pmax}, {k, j + 1, pmax}, {l, k + 1, pmax}]]], IntegerQ[#/2] && # <= Last[ps] &]/2];
A389640list[11] (* Paolo Xausa, Oct 25 2025 *)

Crossrefs

Cf. A389638, A389639, A001248.

Sequence in context: A107838 A095637 A023059 * A015165 A160918 A145578

Adjacent sequences: A389637 A389638 A389639 * A389641 A389642 A389643

Keyword

nonn

Author

Peter Luschny, Oct 10 2025

Status

approved