%I #22 Sep 08 2022 08:46:24

%S 0,16,144,288,576,1152,1600,2304,3328,3600,4624,5184,7056,8352,10368,

%T 10656,10816,11808,12112,12240,12544,13120,13840,16704,17424,19600,

%U 19728,20736,20752,21312,21904,22048,23200,24480,24784,25920,27792,28960,29520,29824,30976,31264,32400

%N Numbers k such that each of k, k+1, k+2, and k+4 is a sum of two squares.

%C All terms are divisible by 16. - _Robert Israel_, Oct 10 2019

%H Robert Israel, <a href="/A328224/b328224.txt">Table of n, a(n) for n = 1..10000</a>

%p ss:= proc(n) option remember;

%p andmap(t -> t[2]::even or t[1] mod 4 <> 3, ifactors(n)[2])

%p end proc:

%p select(k -> ss(k) and ss(k+1) and ss(k+2) and ss(k+4), 16*[$0..10^4]); # _Robert Israel_, Oct 10 2019

%t ok[n_] := AllTrue[{0,1,2,4}, SquaresR[2, #+n] > 0 &]; Select[ Range[0, 32400], ok] (* _Giovanni Resta_, Oct 08 2019 *)

%o (Magma) [k:k in [0..33000]| forall{k+a: a in [0,1,2,4]|NormEquation(1, k+a) eq true}]; // _Marius A. Burtea_, Oct 08 2019

%Y Cf. A001481, A140612, A304441.

%Y Intersection of A082982 and A328223.

%K nonn

%O 1,2

%A _Max Alekseyev_, Oct 08 2019