[seqfan] Re: As much as I hate "base" sequences...

[M. F. Hasler]

On Sat, Jan 18, 2014 at 1:49 PM, Neil Sloane <njasloane at gmail.com> wrote:
> another version which is also nice: restrict the search to numbers which
> eventually reach 1.
> Of those, take the smallest that takes n steps to reach 1. That is a(n).

It seems that no-one yet submitted a(n) =
Number of iterations of A235600 to reach 1 when starting with n, or -1
if 1 is never reached,
where A235600(x) = x/sum_of_digits(x) if this is an integer, else x.

So I propose it as https://oeis.org/draft/A236338

Maximilian



> On Fri, Jan 17, 2014 at 7:26 PM, David Wilson <davidwwilson at comcast.net>wrote:
>
>> Start with k and repeatedly apply the function
>>
>> k -> k / sum of digits of k
>>
>> stopping when there is a positive remainder or the divisor is 1.
>>
>> The smallest survivors of n iterations among the 29-smooth numbers are
>>
>> 0 1
>> 1 2
>> 2 12
>> 3 108
>> 4 1944
>> 5 52488
>> 6 1102248
>> 7 44641044
>> 8 1008000000
>> 9 10080000000
>> 10 100800000000
>> 11 1008000000000
>> 12 10080000000000
>> 13 100800000000000
>> 14 1008000000000000
>> 15 10080000000000000
>> 16 100800000000000000
>> 17 1008000000000000000
>> 18 10080000000000000000
>>
>> I am all but certain that these are these are indeed the smallest survivors
>> among the integers, and that the sequence extends to infinity in the
>> obvious
>> way.
>>
>> The change in behavior at a(8) surprised me at first. a(1) through a(7)
>> eventually reach 1.  For n >= 8, we have
>>
>> a(n) = 1008*10^(n-2) ->  112*10^(n-2) -> 28*10^(n-2) -> 28*10^(n-3) -> ...
>> -> 28.
>>
>> ending at 28 after n iterations.