A234348 Numbers k such that both distances from k to two nearest cubes are perfect cubes.

0, 1, 152, 189, 513, 728, 5859, 6832, 64008, 68913, 150605, 155736, 345744, 355167, 1062936, 1090999, 1481571, 1520848, 6653933, 6742008, 7665056, 7742709, 9667693, 9796248, 15253056, 15438185, 16582104, 16592023, 16766568, 16776487, 26201448, 26460217, 28672299

Offset: 1

Author

Alex Ratushnyak, Dec 24 2013

Keywords

• nonn

Comments

Except a(1)=0, a(n) are numbers k such that both k-x and y-k are perfect cubes, where x and y are two nearest to k cubes: x < k <= y.

Examples

			152 is in the sequence because the following are cubes: 152-125=27 and 216-152=64, where 125 and 216 are the nearest to 152 cubes.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000578, A234334.

Programs

C

#include 
#include    // gcc -O3 A234348.c -lgmp
int main() {
  long long in=0;
  mpz_t n, r, i;
  mpz_init(r);
  mpz_init(i);
  mpz_init_set_ui(n, in);
  while (in < (1ULL<<32)) {
    if (mpz_root(r, n, 3) && in)  mpz_sub_ui(r, r, 1);
    mpz_mul(i, r, r);
    mpz_mul(i, i, r);
    mpz_sub(i, n, i);
    if (mpz_root(i, i, 3)) {
      mpz_add_ui(r, r, 1);
      mpz_mul(i, r, r);
      mpz_mul(i, i, r);
      mpz_sub(i, i, n);
      if (mpz_root(i, i, 3))  printf("%llu, ", in);
    }
    mpz_add_ui(n, n, 1);
    if ((++in&0xfffff)==0)  printf(".");
  }
  return 0;
}