A038853 Numbers that are divisible by 5 and are the difference between two (different positive) cubes in at least one way.

215, 335, 485, 665, 875, 1115, 1330, 1385, 1685, 1720, 2015, 2170, 2375, 2680, 2765, 3185, 3250, 3635, 3880, 4095, 4115, 4570, 4625, 4905, 5165, 5320, 5735, 5805, 6130, 6335, 6795, 6965, 7000, 7625, 7875, 7930, 8315, 8920, 9035, 9045, 9260, 9785, 9970

Offset

1,1

Links

Table of n, a(n) for n=1..43.

Formula

A number is in this sequence iff it is of the form (k+5j)^3-k^3, where k,j are any positive integers, since (k+d)^3 - k^3 = d(3(k+d/2)^2+d^2/4) = 0 (mod 5) iff d=0 (mod 5), since 3x^2 =-y^2/4 (mod 5) iff x=y=0 (mod 5). - M. F. Hasler, Jun 07 2007

Mathematica

With[{nn=50}, Take[(#[[1]]+5#[[2]])^3-#[[1]]^3&/@Tuples[Range[nn], 2]// Union, nn]] (* Harvey P. Dale, Jan 24 2019 *)

Prog

(PARI) A038853(Nmax=10^4, a=[]) = { local(t, j5); for(j=1, Nmax^(1/3)/5, j5=5*j; for(k=1, sqrt((Nmax/j5-j5^2-3*j5)/3), if(Nmax<t=(k+j5)^3-k^3, next); a=concat(a, t))); vecsort(a) } \\ M. F. Hasler, Jun 07 2007

Crossrefs

Sequence in context: A181008 A191943 A046011 * A038860 A120536 A043391

Adjacent sequences: A038850 A038851 A038852 * A038854 A038855 A038856

Keyword

nonn

Author

Jeff Burch

Extensions

Corrected by M. F. Hasler, Jun 07 2007

Status

approved