A079794 hard?

[Maximilian Hasler]

I went through the "uned & more & hard" and now apart from the "smooth
power" series there are only 2 left.

The simplest is the following one:
%S A079794 1,212,132323,1243423434
%N A079794 Smallest number using one 1, two 2's, three 3's, ..., n n's
such that all the digits of r, 1 < r < n are together but two r's are
not adjacent.
%C A079794 How many such numbers can be formed?

The definition is not clear (probably that's why it's uned).
Do you also think it means:
"smallest number having k digits "k", k=1,..,n, but any two adjacent
digits different"
?
Then it's not hard but easy :
1/ start at the beginning with an empty string and always concatenate
the smallest possible of the remaining digits, until there are 2n-1
digits left (the n "n"s and n-1 other digits).
2/ insert the n-1 other digits in-between the "n"s and concatenate
this result to the first string.

However, this gives me for the 4th term:
1223334444 -> 123 233 4444 -> 1234243434
which differs from the given one
(of course its smaller since it's the smallest ;-)
Since there are several odds ( "together" in def, kw hard, different
4th term...) I can imagine I miss something... please confirm.


PS: the sequence corresponding to my definition should go on (mod typo):
123234 535454545
1232343454 64656565656
123234345454565 7576767676767
123234345454565656767 868687878787878
1232343454545656567676767878 97979898989898989

then one could continue with A's, B's or so... (the terms of the
sequence dont actually depend on the base, the property of
"minimality" is "universal").
One could even add "in base n+1" and simply concatenate "digits" with
more than 1 digit for n>10 (would there ever be ambiguity, taking into
account  the property of the first digits remaining the same for
subsequent terms ?
if so, use a coding system for digits > 9, e.g. pre-pend them with a
'0n' where n is the length of the "digit" in characters).

Also, the question in %C is not 100% clear, probably it should mean
"...(non-minimal)..."?

Finally I think this sequence is "less" at least in the sense
"..probably not the one you are looking for".

Maximilian


%I A079794
%S A079794 1,212,132323,1243423434
%N A079794 Smallest number using one 1, two 2's, three 3's, ..., n n's
such that all the digits
               of r, 1 < r < n are together but two r's are not adjacent.
%C A079794 How many such numbers can be formed?
%e A079794 a(3) = 132323 using 1, 2,2, and 3,3,3 with no two adjacent
numbers same.
%Y A079794 Adjacent sequences: A079791 A079792 A079793 this_sequence
A079795 A079796 A079797
%Y A079794 Sequence in context: A082828 A083962 A007942 this_sequence
A092126 A085309 A092127
%K A079794 base,hard,more,nonn,uned
%O A079794 1,2
%A A079794 Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Feb 05 2003




Seqfans, 
Maximilian and Max made some excellent suggestions in email to me.

I sent them the following reply.

Neil



Max, Maximilian:

I appreciate your suggestions, and perhaps one day
I will be able to implement them.

But, as you know, maintaining the OEIS is just something I do
in my spare time, and this summer I will have very little 
and to take care of updates.  That I can take care of!

Anything more than that will have to wait a bit, I'm afraid!

Best regards

Neil