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A328224 Numbers k such that each of k, k+1, k+2, and k+4 is a sum of two squares.

%I A328224 #22 Sep 08 2022 08:46:24
%S A328224 0,16,144,288,576,1152,1600,2304,3328,3600,4624,5184,7056,8352,10368,
%T A328224 10656,10816,11808,12112,12240,12544,13120,13840,16704,17424,19600,
%U A328224 19728,20736,20752,21312,21904,22048,23200,24480,24784,25920,27792,28960,29520,29824,30976,31264,32400
%N A328224 Numbers k such that each of k, k+1, k+2, and k+4 is a sum of two squares.
%C A328224 All terms are divisible by 16. - _Robert Israel_, Oct 10 2019
%H A328224 Robert Israel, <a href="/A328224/b328224.txt">Table of n, a(n) for n = 1..10000</a>
%p A328224 ss:=  proc(n) option remember;
%p A328224   andmap(t -> t[2]::even or t[1] mod 4 <> 3, ifactors(n)[2])
%p A328224 end proc:
%p A328224 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 A328224 ok[n_] := AllTrue[{0,1,2,4}, SquaresR[2, #+n] > 0 &]; Select[ Range[0, 32400], ok] (* _Giovanni Resta_, Oct 08 2019 *)
%o A328224 (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 A328224 Cf. A001481, A140612, A304441.
%Y A328224 Intersection of A082982 and A328223.
%K A328224 nonn
%O A328224 1,2
%A A328224 _Max Alekseyev_, Oct 08 2019