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

1,2

Comments

A subsequence of A234334.

Links

Table of n, a(n) for n=1..38.

Example

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.

Prog

(C)
#include <stdio.h>
#include <math.h>
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<r)  r = rp;
      if (isSquare(r))  printf("%llu, ", n);
    }
  }
  return 0;
}

Crossrefs

Cf. A000290, A234334.

Sequence in context: A266962 A126955 A091105 * A071902 A211412 A052199

Adjacent sequences: A234332 A234333 A234334 * A234336 A234337 A234338

Keyword

nonn

Author

Alex Ratushnyak, Dec 23 2013

Status

approved