[seqfan] Re: Sequence of digit sum divisibility

[Matthijs Coster]

Charles,

Such numbers are about the Niven (or Harshad) numbers. The difference is 
the omittion of "0".
See A005349 (http://oeis.org/A005349).

Greetings,
Matthijs Coster


Op 15-10-2012 22:34, Charles Greathouse schreef:
>> The first of those doesn't show up in a Google search, leading me to
>> believe that this sequence has never been investigated.
> It doesn't seem to be in the OEIS, or at least 142813628717821 and
> 2341207028161 don't appear.
>
>> First, is this of interest for OEIS?
> Yes!
>
> Charles Greathouse
> Analyst/Programmer
> Case Western Reserve University
>
> On Fri, Oct 12, 2012 at 10:02 PM, Jack Brennen <jfb at brennen.net> wrote:
>> Today, I saw a problem posed as such:
>>
>>     "Prove that there are infinitely many numbers not containing the digit 0,
>> that are divisible by the sum of their digits."
>>
>>     Source:  http://www.scribd.com/doc/50712437/Number-Theory
>>     Problem 5.2.3
>>
>> The proposed solution was to prove by induction that (10^(3^n)-1)/9 is such
>> a number for any n>=0.
>>
>>
>> However, I started thinking about constellations of such numbers.
>> Obviously, you can only have nine consecutive such numbers,
>> the first such 9-tuple being the "trivial" (1,2,3,4,5,6,7,8,9).
>>
>> The next such 9-tuples seem to be those starting with:
>>
>> 142813628717821
>> 253323932621811
>> 1234954171531131
>> 1713763544613181
>> 3713154346661821
>> 5953112416611411
>> 8711631351783421
>> 11853531183574141
>> 12191214257422251
>> 17137635446131261
>> 19941476493818971
>> 21342541323383331
>> 25628491758925521
>> 28665872459864731
>> 32674635925331471
>> 33637395433589721
>> 38442737638388241
>> 43566181233775271
>> 45122116277838671
>> 47715341351277671
>> 56411383343515261
>> 59265887192515161
>> 64311981821287271
>> 69171996587934331
>> 69795167728366171
>> 75283694541843561
>> 75722172144418871
>> 79871332261921271
>> 81118141111687741
>> 84539137394111471
>> 89699721156239121
>> 92318812614428471
>> 94542622211157181
>> 96591526766935291
>> 96694399875626381
>>
>> The first of those doesn't show up in a Google search, leading me to believe
>> that this sequence
>> has never been investigated.
>>
>> First, is this of interest for OEIS?  Second, if so, can somebody verify
>> that those are correct?
>>
>>    Jack
>>
>> _______________________________________________
>>
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