[seqfan] Re: From N to a palindrome by adding

[Neil Sloane]

Eric Angelini's recent inventions are very nice indeed,
and I created http://oeis.org/A241173 through A241183. Many of them need
more terms, and in a couple of cases
the "Records" sequences also need to be added.
Eric, as always, thank you for these ideas.
Neil


On Sun, Apr 20, 2014 at 3:36 PM, Eric Angelini <Eric.Angelini at kntv.be>wrote:

>
> Hello SeqFans,
> Start from any integer N and try to reach
> a palindromic number in as few steps as possible.
> A step is an addition -- you add to N one of N's
> digits. And you iterate from there.
> I've computed what I think are the shortest (?)
> paths for 1 to 25 (in a condensed
> way).
>
> [Some possible sequences after the list,
> if the idea is not old hat.]
>
> 1+1=2
> 2+2=4
> 3+3=6
> 4+4=8
> 5+5=10+1=11
> 6+6=12+1=13+3=16+6=22
> 7+7=14+1=15+1=16+6=22
> 8+8=16+6=22
> 9+9=18+1=19+1=20+2=22
> 10+1=11
> 11+1=12+1=13+3=16+6=22
> 12+1=13+3=16+6=22
> 13+3=16+6=22
> 14+1=15+1=16+6=2
> 15+1=16+6=22
> 15+5=20+2=22
> 16+6=22
> 17+7=24+4=28+2=30+3=33
> 18+1=19+1=20+2=22
> 19+1=20+2=22
> 20+2=22
> 21+1=22
> 22+2=24+4=28+2=30+3=33
> 23+2=25+5=30+3=33
> 24+4=28+2=30+3=33
> 25+5=30+3=33
> ...
>
> Questions:
> 1) how many steps does 2014 need to reach
> a palindrome?
> 2) is there a general formula?
> 3) some sequences might be of interest
> for the OEIS:
> - smallest integer reaching a palindrome
> in n steps;
> - smallest integer reaching a palindrome
> in n different ways (15 is an example above);
> ...
> Best,
> É.
>
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>



-- 
Dear Friends, I have now retired from AT&T. New coordinates:

Neil J. A. Sloane, President, OEIS Foundation
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
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