A234335 Numbers k such that distances from k to three nearest squares are three perfect squares.

0, 5, 65, 160, 325, 1025, 2501, 5185, 5525, 7200, 9605, 16385, 26245, 40001, 40885, 58565, 82945, 93925, 97920, 114245, 153665, 160225, 187200, 202501, 204425, 219385, 262145, 334085, 419905, 430625, 521285, 640001, 707200, 777925, 781625, 869465, 937025, 972725

Offset: 1

Author

Alex Ratushnyak, Dec 23 2013

Keywords

• nonn

Comments

A subsequence of A234334.

Examples

			5 is in the sequence because the following three are perfect squares: 5-4=1, 5-1=4, 9-5=4.
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.
		

Crossrefs

Cf. A000290, A234334.

Programs

C

#include 
#include 
typedef unsigned long long U64;
U64 isSquare(U64 a) {
  U64 r = sqrt(a);
  return r*r==a;
}
int main() {
  for (U64 n=0; ; ++n) {
    U64 r = sqrt(n);
    if (r*r==n && n)  --r;
    if (isSquare(n-r*r) && isSquare((r+1)*(r+1)-n)) {
      U64 rp = (r+2)*(r+2)-n;
      r = n-(r-1)*(r-1);
      if (n<=1 || rp
				

Mathematica

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 *)