OEIS on vacation in December

[Jonathan Post]

I don't actually disagree with Henry Bottomley, whose sequences are
beautiful. I'm trying to say that one can make lemonade out of lemons.  Zak
recently compalined over the sequence of 10*triangular numbers, parallel to
what Henry just said about "ten times A099676.  The final zeros do not add
to its interest." However, trying to lemonade out of lemons, I first looked
at primes which were +1 or -1 from 10*triangular numbers, which njas used
reluctantly.  Looking deeper, this led to a bunch of seqs (7 or 8 so far)
which Robert W. Wilson v is about to submit.

Similarly, I've just submitted comments on what I think are beautiful
connections between the so-simple A003983 which njas just re-edited, where
the array's row sums are A005900 octahedral numbers; and on the so-simple
A124171 whose array's row sums' records are A006003 n(n^2+1)/2.

The OEIS is both results and raw materials for sometimes deeper results.

Looking deeply at simple things leads to, for instance, the ABC conjecture.
So, as I say, beautiful is as beautiful does.

-- Jonathan Vos Post

On 12/5/06, Henry <se16 at btinternet.com> wrote:
>
> Jonathan Post wrote:
>
> > Beautiful is, as I've said, subjective.  It partly depends on what one
> > does with it. It partly depends on the depth of the mathematical
> > theory. Even for "base" sequences. To me, for insdtance, this is
> > slightly pretty, although spawned from something apparently dull and
> base.
> >
> > Partial sums of A124167
> > 90, 1080, 11070, 111060, 1111050, 11111040, 111111030, * *1111111020,
> > 11111111010, 111111111000, 1111111110990,* *...
> >
> > example:
> >
> > **a(8) = 90 + 990 + 9990 + 99990 + 999990 + 9999990 + 99999990 +
> > 999999990 = 1111111020.
> >
> > How does this generalize over bases other than 10?
> >
> > -- Jonathan Vos Post
>
> It is not particularly interesting because it is simply ten times
> A099676.  The final zeros do not add to its interest.
>
> Henry Bottomley
>
>
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