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

[Eric Angelini]

Please note that 101 requires one step to
reach a palindrome: 101+0=101

There are two solutions (at least) for 17:
17+7=24+4=28+2=30+3=33
17+1=18+1=19+1=20+2=22

... which might generate another sequence:
- numbers reaching two different palindromes 
in the same number of steps 
(I guess _three_ palindromes_ are out
of reach)

> Le 20 avr. 2014 à 21:37, "Eric Angelini" <Eric.Angelini at kntv.be> a écrit :
> 
> 
> 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.
> 
> 
> 
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