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

%I A234348 #10 Jan 08 2014 13:47:26
%S A234348 0,1,152,189,513,728,5859,6832,64008,68913,150605,155736,345744,
%T A234348 355167,1062936,1090999,1481571,1520848,6653933,6742008,7665056,
%U A234348 7742709,9667693,9796248,15253056,15438185,16582104,16592023,16766568,16776487,26201448,26460217,28672299
%N A234348 Numbers k such that both distances from k to two nearest cubes are perfect cubes.
%C A234348 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 A234348 Donovan Johnson, <a href="/A234348/b234348.txt">Table of n, a(n) for n = 1..1000</a>
%e A234348 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 A234348 (C)
%o A234348 #include <stdio.h>
%o A234348 #include <gmp.h>   // gcc -O3 A234348.c -lgmp
%o A234348 int main() {
%o A234348   long long in=0;
%o A234348   mpz_t n, r, i;
%o A234348   mpz_init(r);
%o A234348   mpz_init(i);
%o A234348   mpz_init_set_ui(n, in);
%o A234348   while (in < (1ULL<<32)) {
%o A234348     if (mpz_root(r, n, 3) && in)  mpz_sub_ui(r, r, 1);
%o A234348     mpz_mul(i, r, r);
%o A234348     mpz_mul(i, i, r);
%o A234348     mpz_sub(i, n, i);
%o A234348     if (mpz_root(i, i, 3)) {
%o A234348       mpz_add_ui(r, r, 1);
%o A234348       mpz_mul(i, r, r);
%o A234348       mpz_mul(i, i, r);
%o A234348       mpz_sub(i, i, n);
%o A234348       if (mpz_root(i, i, 3))  printf("%llu, ", in);
%o A234348     }
%o A234348     mpz_add_ui(n, n, 1);
%o A234348     if ((++in&0xfffff)==0)  printf(".");
%o A234348   }
%o A234348   return 0;
%o A234348 }
%Y A234348 Cf. A000578, A234334.
%K A234348 nonn
%O A234348 1,3
%A A234348 _Alex Ratushnyak_, Dec 24 2013