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

 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 #include #include #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

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.

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