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A234348 Numbers k such that both distances from k to two nearest cubes are perfect cubes. 2

%I

%S 0,1,152,189,513,728,5859,6832,64008,68913,150605,155736,345744,

%T 355167,1062936,1090999,1481571,1520848,6653933,6742008,7665056,

%U 7742709,9667693,9796248,15253056,15438185,16582104,16592023,16766568,16776487,26201448,26460217,28672299

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

%C 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.

%H Donovan Johnson, <a href="/A234348/b234348.txt">Table of n, a(n) for n = 1..1000</a>

%e 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.

%o (C)

%o #include <stdio.h>

%o #include <gmp.h> // gcc -O3 A234348.c -lgmp

%o int main() {

%o long long in=0;

%o mpz_t n, r, i;

%o mpz_init(r);

%o mpz_init(i);

%o mpz_init_set_ui(n, in);

%o while (in < (1ULL<<32)) {

%o if (mpz_root(r, n, 3) && in) mpz_sub_ui(r, r, 1);

%o mpz_mul(i, r, r);

%o mpz_mul(i, i, r);

%o mpz_sub(i, n, i);

%o if (mpz_root(i, i, 3)) {

%o mpz_add_ui(r, r, 1);

%o mpz_mul(i, r, r);

%o mpz_mul(i, i, r);

%o mpz_sub(i, i, n);

%o if (mpz_root(i, i, 3)) printf("%llu, ", in);

%o }

%o mpz_add_ui(n, n, 1);

%o if ((++in&0xfffff)==0) printf(".");

%o }

%o return 0;

%o }

%Y Cf. A000578, A234334.

%K nonn

%O 1,3

%A _Alex Ratushnyak_, Dec 24 2013

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Last modified October 23 16:20 EDT 2021. Contains 348215 sequences. (Running on oeis4.)