is this sequence interesting?

[Matthijs Coster]

Dear Peter,

This sequence is related to
http://www.research.att.com/~njas/sequences/A118235,
http://www.research.att.com/~njas/sequences/A109814, some other sequences...
since t(k)-t(j) is the sum of k-j consecutive positive integers (j+1 ... k).

Kind regards,

Matthijs Coster


> I think it's a great sequence.  Of course/unfortunately there are
> several other sequences that should be submitted along with it: the
> sequence of the corresponding j, of the t(k), and of the t(j) -- I
> think all four should be in there with the relevant cross-refs.
>
> While you're at it, you might check "number of ways of writing n as
> the difference of two triangular numbers" and make sure that it's in
> OEIS also.
>
> Thanks,
> --Joshua
>
> On Sat, Mar 29, 2008 at 7:42 PM, Peter Pein <petsie at dordos.net> wrote:
>   
>>  let t(k)=k*(k+1)/2 be the k-th triangular number and write n>=2 as difference
>>  of two positive triangular numbers: n = t(k) - t(j).
>>
>>  Now define a(n) as the minimal k needed for the minuend:
>>
>>  a(n) := min(k > 0: there exists j>0 with n = t(k)-t(j) )
>>  example:
>>
>>   a(30)=8, because 30 = t(30) - t(29)
>>                       = t(11) - t( 8)
>>                       = t( 9) - t( 5)
>>                       = t( 8) - t( 3)
>>
>>  and t(8) is the smallest minuend.
>>
>>  The sequence starts (with offset 2,1):
>>
>>      2,  3,  4,  3,  6,  4,  8,  4, 10,
>>   6,  5,  7,  5,  6, 16,  9,  6, 10,  6,
>>   8,  7, 12,  9,  7,  8,  7, 28, 15,  8,
>>  16, 32,  8, 10,  8, 13, 19, 11,  9, 10,
>>  21,  9, 22,  9, 10, 13, 24, 17, 10, 12,
>>  11, 10, 27, 10, 13, 11, 12, 16, 30, 11,
>>  31, 17, 11, 64, 11, 18, 34, 12, 14, 13,
>>  36, 12, 37, 20, 12, 13, 12, 21, 40, 18,
>>  13, 22, 42, 14, 13, 23, 17, 13, 45, 13,
>>  16, 15, 18, 25, 14, 33, 49, 17, 14, 16
>>     
>
>