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%I #12 Jul 10 2024 20:05:55
%S 215,335,485,665,875,1115,1330,1385,1685,1720,2015,2170,2375,2680,
%T 2765,3185,3250,3635,3880,4095,4115,4570,4625,4905,5165,5320,5735,
%U 5805,6130,6335,6795,6965,7000,7625,7875,7930,8315,8920,9035,9045,9260,9785,9970
%N Numbers that are divisible by 5 and are the difference between two (different positive) cubes in at least one way.
%F 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
%t With[{nn=50},Take[(#[[1]]+5#[[2]])^3-#[[1]]^3&/@Tuples[Range[nn],2]// Union,nn]] (* _Harvey P. Dale_, Jan 24 2019 *)
%o (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
%K nonn
%O 1,1
%A _Jeff Burch_
%E Corrected by _M. F. Hasler_, Jun 07 2007