OEIS on vacation in December

[Nick Hobson]

At this point I should hold up my hand and admit that I recently submitted  
a sequence -- http://www.research.att.com/~njas/sequences/A125239 -- that  
relates to 10*triangular numbers!  Neil mildly chastised me at the time,  
and mentioned that triangular numbers had recently been discussed on this  
forum!  I hadn't noticed that 10T(n) had just been added to the database,  
so I didn't crossreference that sequence.  What interested me was that all  
divisors of 10T(n)+1 are congruent to +/-1, mod 10.  Ditto a similar  
result for 6T(n)+1, whose divisors are always = 1 mod 6.  However, I  
accept that the resulting sequences ("smallest prime divisor such  
that...") are slightly forced and maybe of borderline interest.  Perhaps  
the comment I added to http://www.research.att.com/~njas/sequences/A062786  
would have been sufficient?

Similarly, it can be shown that all prime divisors of T(n)+1 different  
 from 2 and 7 are congruent to 1, 9, 11, 15, 23, or 25, mod 28.  I promise  
not to make a sequence out of that factoid!

I'm still trying to get a handle on what can make a "good" sequence.   
Underlying mathematical concepts provide one obvious criterion.  Also,  
Neil has said (http://www.research.att.com/~njas/sequences/Spuzzle.html)  
he would like the OEIS to serve as a repository of published puzzle  
sequences.  Then there are sequences such as  
http://www.research.att.com/~njas/sequences/A115921 (numbers n such that  
the digits of phi(n) are a permutation of those of n, in base 10), that  
may have been submitted in response to a programming challenge.  A variant  
of the puzzle sequence, I suppose.

Nick


On Tue, 05 Dec 2006 21:10:05 -0000, Jonathan Post <jvospost3 at gmail.com>  
wrote:

> 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
>>
>>