[seqfan] Two make a palindrome
Eric Angelini
Eric.Angelini at kntv.be
Sat Nov 9 11:07:10 CET 2013
Hello SeqFans,
this seq P is so nice that I was almost
in tears all night ;-)
[and I'm convinced that P is a
permutation of the non-negative
integers 0,1,2,3,4,5... +oo though
it is far from being obvious (I might
be overoptimistic)]:
P=0,11,1,10,100,12,2,20,101,22,3,13,31,103,30,110,40,...
The trick:
Take any pair of neighbouring terms;
you can build a palindrome including all the digits of the pair.
Start with a(1)=0 then extend P
with the smallest unused integer
that fits the requirement.
0 and 11 could produce 101, which
is a palindrome;
11 and 1 produce 111
1 and 10 produce 101
10 and 100 produce 10001
100 and 12 produce 10201
12 and 2 produce 212
2 and 20 produce 202
20 and 101 produce 10201
101 and 22 produce 12021
etc.
Extending P by hand is very
confusing -- but incredibly fun --
please excuse any potential mistake.
Best,
É.
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