[seqfan] Re: Which of these two definitions is better?

[Ali Sada]

  Hi Dr. Hasler,
 Thank you for your response.  Maybe this definition would be more specific: "Least multiple of n that contains only the digits of n and n+1. Each digit should appear at least once." 

 I think that in this sequence we avoid the problem of powers of 2 and powers of 5, mentioned by David Seal. 
 For example, 128=2^7.  We can find a multiple of 128 that contains 9 by repeating 128 until we reach the 8th digit, or higher,  then we put 9.    
 98128128 is a multiple of 128. However, are we sure this method will give us the "least multiple"?  

  Maybe we could add another sentence to make sure that we have values for all numbers. Something like "Add the least number of extra digits when necessary." 

 As  for the glued together words, this happens only when I send emails to the Seqfan list. This time, I left a space before and after each line, as you advised. 
 
 It seems that other people who use Word face the same problem. 

  https://answers.microsoft.com/en-us/msoffice/forum/all/formatting-gets-distorted-in-word-files-after/426a480e-572b-4e89-a268-9e898391dfee



 Best, 

 Ali 

  

    On Monday, November 18, 2019, 8:36:15 AM EST, M. F. Hasler <seqfan at hasler.fr> wrote:  
 
 Ali,given the ambiguities that arose earlier, you should not use "consists of the digits"but be more explicit :- must contain every digit of ...(not taken with multiplicity) *at least once* and no other digits  ?
because it is unclear:- must every digit of n,n+1 occur? (we know: "yes" ! => "every")- can digits be re-used ?  (if n, n+1 have only one '0', can the multiple have several '0's ?)- must digits be used as many times as there are present ?  (if n, n+1 have two '1's, must the multiple have exactly/al least two '1's ?) Thanks.
PS: could you please also make an effort to avoid the "glued together" words in your message?("changedthe" , "twoversions" , "theleast", "optionalextra" , "havethe" , "butsince" , "digitswhen" ...)for example , start and/or end  each  line with a space if necessary.It is  confusing and  unpleasant to read.-- 
Maximilian
On Sun, Nov 17, 2019 at 10:35 PM Ali Sada via SeqFan <seqfan at list.seqfan.eu> wrote:

Hi Everyone,

I changedthe sequence I sent earlier and made it more straightforward. It has twoversions now. 


 
Version 1:"a(n) is theleast multiple of n that consists of the digits of n, n+1, and an optionalextra digit."
 

Data: 12, 32,234, 504, 65, 276, 287, 928, 189, 10, 121, 132, 143, 154, 165, 176, 187, 198, 209,120, 210, 132, 2346, 2544, 625, 2678, 1728, 2968

 

Here, we havethe option of not using the extra digit. We add it if it gives us a smaller valueof a(n). For example, without an extra digit, a(9) should be 10111111119. Butsince we have the option of adding the extra digit, a(9) is 189.  

 
Version 2:

"a(n) is theleast multiple of n that consists of the digits of n and n+1. Add an extra digitwhen necessary." 

 

Data: 12, 32,4443, 544, 65, 7776, 8888887, 9888, 10111111119, 10, 121, 132, 143, 154, 165, 176,187, 198, 209, 120, 210, 2332.

 
In thisversion, we can use the extra digit only when we can’t have a value for a(n)without it. 

 
In bothversions, I still don’t know if we can have values for all n. 

In case oneof these sequences is suitable for the OEIS, I need some help calculating the terms!

Best,

 

Ali