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.
