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A234348 Numbers k such that both distances from k to two nearest cubes are perfect cubes. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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.

LINKS

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

EXAMPLE

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.

PROG

(C)

#include <stdio.h>

#include <gmp.h>   // 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;

}

CROSSREFS

Cf. A000578, A234334.

Sequence in context: A200934 A174759 A289821 * A185394 A097640 A253367

Adjacent sequences:  A234345 A234346 A234347 * A234349 A234350 A234351

KEYWORD

nonn

AUTHOR

Alex Ratushnyak, Dec 24 2013

STATUS

approved

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Last modified September 21 16:31 EDT 2021. Contains 347598 sequences. (Running on oeis4.)