[seqfan] Re: Triangular numbers, such that the difference of theirs two (not-equal) largest prime factors is also (smaller) triangular number

[Charles Greathouse]

36795331 -> 3916 -> 78 -> 10 -> 3

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Tue, Sep 29, 2009 at 11:27 AM, Alexander Povolotsky
<apovolot at gmail.com> wrote:
> Hi,
>
> Consider sequence(s?) of the triangular numbers, such that the
> difference of theirs two (not-equal - with the exclusion for "factors"
> of 1 ) largest prime (or 1 - only when it comes to deal with the
> "factors" of 1 ) factors is producing also (but of course smaller)
> triangular number
>
> Going backwards (in descending order) I found one such (seems to be
> finite 3 term) sequence
>
> 1, 6, 741
>
> 741 = 3*13*19;  19-13=6
>    6 = 2*3;            3-2=1
>
> Are there any other such sequences (and if such exist - are they all finite ?)
>
> Regards,
> Alexander R. Povolotsky
>
>
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