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%I #7 Jul 03 2024 13:44:07
%S 0,5,65,160,325,1025,2501,5185,5525,7200,9605,16385,26245,40001,40885,
%T 58565,82945,93925,97920,114245,153665,160225,187200,202501,204425,
%U 219385,262145,334085,419905,430625,521285,640001,707200,777925,781625,869465,937025,972725
%N Numbers k such that distances from k to three nearest squares are three perfect squares.
%C A subsequence of A234334.
%e 5 is in the sequence because the following three are perfect squares: 5-4=1, 5-1=4, 9-5=4.
%e 65 is in the sequence because the following three are perfect squares: 65-64=1, 65-49=16, 81-65=16, where 49, 64, 81 are the three squares nearest to 65.
%t ps3Q[n_]:=AllTrue[Take[Sort[Abs[n-(Floor[Sqrt[n]]+{-2,-1,0,1,2})^2]],3],IntegerQ[Sqrt[#]]&]; Join[ {0},Select[Range[2,10^6],ps3Q]] (* _Harvey P. Dale_, Jul 03 2024 *)
%o (C)
%o #include <stdio.h>
%o #include <math.h>
%o typedef unsigned long long U64;
%o U64 isSquare(U64 a) {
%o U64 r = sqrt(a);
%o return r*r==a;
%o }
%o int main() {
%o for (U64 n=0; ; ++n) {
%o U64 r = sqrt(n);
%o if (r*r==n && n) --r;
%o if (isSquare(n-r*r) && isSquare((r+1)*(r+1)-n)) {
%o U64 rp = (r+2)*(r+2)-n;
%o r = n-(r-1)*(r-1);
%o if (n<=1 || rp<r) r = rp;
%o if (isSquare(r)) printf("%llu, ", n);
%o }
%o }
%o return 0;
%o }
%Y Cf. A000290, A234334.
%K nonn
%O 1,2
%A _Alex Ratushnyak_, Dec 23 2013
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