Rhyming digits

[Mitch Harris]

On Dec 3, 2007 1:18 PM, Eric Angelini <Eric.Angelini at kntv.be> wrote:
>
> is this seq worth the OEIS?
>
> a(n) is always the smallest integer not yet present in S (="NYPIS")
> and having its last digit equal to the n-st digit of S:
>
> S = 1,11,21,2,31,12,3,41,51,22,51,32,13,4,...
>
> a(1)= 1 is the smallest integer "NYPIS" ending with 1 (1st digit of S)
> a(2)= 11 is the smallest integer ...    ending with 1 (2nd digit of S)
> a(3)= 21 is the smallest integer ...    ending with 1 (3rd digit of S)
> a(4)= 2 is the smallest integer ...     ending with 2 (4th digit of S)
>...
> [Yes, one could start S in many different ways:
>  S= 9,8,7,6,5,4,3,2,1, then 11,21,12,31,...
>  S= 1,3,5,7,9,2,4,6,8, then 11,21,12,31,...
>  S= 1,2,3,4,5,6,7,8,9, then 11,21,12,31,...]

It's interesting in that it has precedents in the OEIS, but it has the
digit base as a parameter as well as the initial conditions.

Is S defined as the digit concatenation of a(1), a(2), a(3), etc...?
Then S doesn't seem well defined unless the initial conditions are of
a certain form (a(1) and a(2) have at least 3 digits between them).

To answer your question about whether it is worth the OEIS, if you can
give some kind of  formula or say something non-trivial about it, then
it might be worth it. But Neil has time constraints, so come up with
something non-trivial before sending it in. Is there something special
about base 10 here.

As a general side suggestion (not necessarily relevant here), I'd bet
that almost every sequence in the OEIS that has keyword 'base' and
works on base 10 would be -much- more interesting if done base 2. (but
that's not to say that the latter is itself actually interesting, just
more so than for base 10).

So, if you do it base 10, also try it base 2; you'll be more likely to
see interesting patterns.
-- 
Mitch Harris