[seqfan] Re: Strings resurrection

[Maximilian Hasler]

Dear Eric, dear SeqFans,

I have created http://oeis.org/A216556 :
Concatenate decimal digits of n, each increased by 1.
(approved by Joerg Arndt),
and http://oeis.org/drafts/A216557 :
Number of iterations of A216556 until the initial value n appears
again as a substring; 0 if this will never happen.
which starts (offset=0):
10,9,9,9,9,9,9,9,9,9,9,19,28,37,46,55,64,73,82,90,

Already A216557(20) seems to take an infinite time (>20 sec) to compute,
maybe s/o can show it's 0 ?
Should the same be true for n=127 ?
I found A216557(27)=64 .
I remarked that that "27" appeas in the 214 digit number
A216556^{64} (27) =
322121102110109211010910998
211010910998109989887
211010910998109989887
1099898879887877687767
6657
66565547
6656554655454437
66565546554544365545443544343327
665655465545443655454435443433265545443544343325443433243323221.

I think this pattern can be analyzed and the value of A216557(27)
and other interesting properties about these maps could be deduced.

Maximilian


On Sat, Sep 8, 2012 at 10:17 AM, Eric Angelini <Eric.Angelini at kntv.be> wrote:
>
> Hello SeqFans,
> Start with n = 127. Replace, one by one, every digit 'd' of n by 'd+1'. Iterate.
> 127 -> 238 -> 349 -> 4510 -> 5621 -> 6732...
> Questions:
> *Will the substring <127> reappear at some stage in the iteration of 127?
> *If yes, after how many steps?
> *Can we assign to n=1, n=2, n=3, etc., the number of steps needed to see the substring <n> reappear in the iteration of n (as defined above)?
> *If we go backwards, we can see that 905 will produce the substring <127> in 2 steps:
> 905 -> 1016 -> 2127 (hit). Is 905 the smallest integer producing 127?
> *What are the smallest "ancestors" of n=1, n=2, n=3, ... producing the substring <n>?
> Best,
> É.
>
>
>
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