d x e = r and now concatenate e and r

[Eric Angelini]

Hello Math-Fun and SeqFans,
still a few hours to go in 2007, in Brussels, Belgium -- and
thus time for our last (uninteresting) seq of the year!

S=1,11,22,24,28,216,318,324,416,424,624,728,756,848,864,
936,954,1144,1248,1296,1378,13104,26104,27108,27216,...

All integers of S are the concatenation of e and r, r being
the "r"esult of (d x e) and d being the last "d"igit of the
previous integer.

Integer a(n+1) must be bigger than a(n) but the gap between
a(n) and a(n+1) must be the smallest possible one.
No integer of S can end with a zero.

Example:

Start with a(1)=1
then d=1 and, obviously, e=1 and r=1 --> S=1,11,...
Now d=1 again and we must take e=2 ; thus r=2 and --> S=1,11,22,...
Now d=2 and the closest integer to the last one (22) can be
found with e=2 ; thus r=4 and --> S=1,11,22,24,...

Etc.

In other words, we multiply the last digit of a(n) by something,
we concatenante the result immediately after this something, and
we look for the smallest integer resulting in this concatenation
but bigger than a(n).

Voilà!

Cheers, happy 2008, mind the headaches!

É.








Dear Seqfans,

Several people have suggested that those
of us who will be attending the Amer Math Soc. / Math Assoc Amer.
meetings in San Diego - and anyone else who is in town -

So what I propose is that we meet in the lobby of the
conference hotel at 5pm on Sunday Jan 06 2008,
and then we decide what to do (go off for pizza and beer

It is a big hotel, so to be specific, let's all
meet in the East Lobby Lounge, lobby level, North Tower,
of the San Diego Marriott Hotel and Marina,
333 West Harbor Drive, San Diego.

Susanna and I are staying at this hotel, which
is the headquarters hotel for the meetings.
Of course you don't have to be attending the meetings
to come to the party! The Gibbs Lecture 
is at 8:30pm (Avi Widgerson: Randomness, A Compational
Complexity View), so by meeting at 5pm anyone who
wants to go to it will be able to do so. 

Please pass this message on to anyone who might
not be on the list.

Looking forward to seeing you in San Diego!

Neil



Plausible programming exercises ... can these be hacked by hand?

A104628:  What 5 integer powers of the golden ratio sum to 2008?

A060667:  What's the GCD of the numbers with Euler totient 2008?