login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A268509 Numbers x such that x^3 = y^2 + z for some y and some nonzero z with -x < z < x. 3
2, 3, 5, 13, 15, 17, 32, 35, 37, 40, 43, 46, 52, 56, 63, 65, 99, 101, 109, 136, 143, 145, 152, 158, 175, 190, 195, 197, 243, 255, 257, 312, 317, 323, 325, 331, 336, 351, 356, 366, 377, 399, 401, 422, 483, 485, 560, 568, 575, 577, 584, 592, 654, 675, 677, 717, 741, 783, 785, 799, 810, 891, 899, 901, 909, 937, 944, 978 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

List of x such as x^3 is a near square (see examples).

Note that z = 17 appears often (see A029728).

LINKS

Daniel Mondot, Table of n, a(n) for n = 1..10000

EXAMPLE

2^3 = 3^2 - 1;

3^3 = 5^2 + 2;

5^3 = 11^2 + 4;

13^3 = 47^2 - 12;

15^3 = 58^2 + 11;

17^3 = 70^2 + 13;

32^3 = 181^2 + 7;

35^3 = 207^2 + 26;

37^3 = 225^2 + 28;

40^3 = 253^2 - 9;

43^3 = 282^2 - 17;

46^3 = 312^2 - 8;

52^3 = 375^2 - 17;

56^3 = 419^2 + 55;

63^3 = 500^2 + 47;

65^3 = 524^2 + 49;

99^3 = 985^2 + 74.

PROG

(C)

#include <stdio.h>

#include <stdlib.h>

#include <math.h>

#define MAX2 10000

/* list number x and y such that x^3 = y^2 ± delta (0 < delta < x) */

/* this generates A268509 and A268510 */

long long unsigned b, c, d;

long long signed ds;

unsigned long long list2[MAX2];

unsigned long long list3[MAX2];

long double b1, cd, dd;

void main(unsigned argc, char *argv[])

{

unsigned a, i;

  i=0;

  // I never actually calculate b^3 or c^2, but only b^(3/2) = c + ds

  // this allows me to indirectly check b^3 past 2^64

  for (b=0; b<100000000; ++b) // could go up to b<4294967295u; max

  {

    b1 = sqrtl(b);

    cd= b1 *(long double)b;

    c=(long long unsigned)(cd+(double)0.5);

    dd = 2 * c * (cd - c);

    if (dd<0) ds = (dd - 0.5);

    else ds = (dd + 0.5);

    d = llabs(ds);

    if (d<b) // d = abs(b^3 - c^2)

    {

      if (ds)

      {

        if (i<MAX2)

        {

          list2[i]= b;

          list3[i++]= c;

        }

      }

    }

  }

  // generate A268509 */

  for (a=0; a<i; ++a) printf("%u %llu\n", a+1, list2[a]);

  printf("\n\n");

  // generate A268510 */

  for (a=0; a<i; ++a) printf("%u %llu\n", a+1, list3[a]);

  printf("\n\n");

}

(PARI) is(n)=my(t=abs(n^3-round(n^1.5)^2)); 0<t && t<n \\ Charles R Greathouse IV, Feb 09 2016

CROSSREFS

Cf. A029728, A253181, A268510.

Sequence in context: A251414 A145343 A058592 * A260594 A228940 A045311

Adjacent sequences:  A268506 A268507 A268508 * A268510 A268511 A268512

KEYWORD

nonn

AUTHOR

Daniel Mondot, Feb 06 2016

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 24 03:22 EST 2020. Contains 332195 sequences. (Running on oeis4.)