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Numbers k such that both k and k+4 are sums of two squares.
1

%I #16 Sep 08 2022 08:46:24

%S 0,1,4,5,9,13,16,25,32,36,37,41,45,49,61,64,68,81,85,97,100,109,113,

%T 117,121,144,145,149,153,160,169,181,193,196,208,221,225,229,241,256,

%U 257,261,265,277,288,289,292,313,320,324,333,349,356,361,365,369,373,388,397,400

%N Numbers k such that both k and k+4 are sums of two squares.

%t ok[n_] := AllTrue[{0, 4}, SquaresR[2, # + n] > 0 &]; Select[Range[0, 400], ok] (* _Giovanni Resta_, Oct 08 2019 *)

%o (Magma) [k: k in [0..400] | NormEquation(1, k) eq true and NormEquation(1, k+4) eq true]; // _Marius A. Burtea_, Oct 08 2019

%Y Subsequence of A001481. Contains A328224 as a subsequence.

%Y Cf. A140612, A082982, A304441.

%K nonn

%O 1,3

%A _Max Alekseyev_, Oct 08 2019