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

Author

Jeff Burch

Keywords

• nonn

Programs

Mathematica

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

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(NmaxM. F. Hasler, Jun 07 2007

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

Extensions

Corrected by M. F. Hasler, Jun 07 2007