Possible Comment on A007095

[Tanya Khovanova]

Yes:
x^3 - y^3 == 0 mod 5 iff x - y == 0 mod 5 (so you're right about A038853).
Also
x^3 - y^3 == 1 mod 2 iff x - y == 1 mod 2
so x^3 - y^3 == 5 mod 10 iff x - y == 5 mod 10 (so you're right about 
A038860).
Perhaps it should be mentioned that here "cubes" means "cubes of positive 
integers", e.g. 65 = 4^3 - (-1)^3 and 125 = 5^3 - 0^3 are not included.

Cheers,
Robert Israel

On Thu, 31 May 2007, Maximilian Hasler wrote:

> at first sight it seems to me as if
> A038860 = { b(k,j) ; k=1,2,3..., j=1,3,5,7... }
> A038853 = { b(k,j) ; k=1,2,3..., j=1,2,3,4... }
> with b(k,j)=(k+5j)^3-k^3
> (and k=0 might be allowed depending on personal idea of cubes)
> but I don't have time to think about "completeness" and since I tend
> to make small errors when I don't have time...
> M.H.
>
> On 5/31/07, Maximilian Hasler <maximilian.hasler at gmail.com> wrote:
>> Definitely, any number of the form 5(3k(k+5)+25) = (k+5)^3-k^3
>> should be in that sequence, and 1385 is of that form.
>> M.H.
>> 
>> On 5/31/07, Tanya Khovanova <tanyakh at tanyakhovanova.com> wrote:
>> > Hello Seqfans,
>> >
>> > Looking at the definitions, A038860 should be a subsequence of A038853; 
>> but 1385 is missing in A038853.
>> >
>> > A038853                  Numbers that are divisible by 5 and are 
>> differences between two cubes in at least one way.
>> >         215, 335, 485, 665, 875, 1115, 1330, 1685, 2015, 2170, 2375, 
>> 2680, 2765, 3150, 3185, 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, 10305
>> >
>> > A038860                  Numbers n such that n ends with '5' and is 
>> difference between two cubes in at least one way.
>> >         215, 335, 485, 665, 875, 1115, 1385, 1685, 2015, 2375, 2765, 
>> 3185, 3635, 4095, 4115, 4625, 4905, 5165, 5735, 5805, 6335, 6795, 6965, 
>> 7625, 7875, 8315, 9035, 9045, 9785, 10305, 10565, 11375, 11655, 12215, 
>> 13085, 13095, 13985, 14625, 14915, 15875
>> >
>> > Tanya
>> >
>> >
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