[seqfan] Re: Fractions, digits, decimal expansion

Neil Sloane njasloane at gmail.com
Tue Dec 15 02:53:50 CET 2015


Bob said: "9 does not appear".

Do you have a proof, or this just a conjecture? [I seem to be asking that a
lot recently!
But in mathematics the distinction is vital.]

Maybe I did not understand the question, but suppose after a while we reach
the number 11111145478227154832
(since the terms must be distinct, the sequence either dies (unlikely here)
or the terms
get bigger and bigger, so after a zillion steps we will see large numbers).

Then the next term could be 9, because 11111145478227154832/9
= 1234571719803017203.5555555555...
and all the digits on the left also appear on the right.

My guess is that every number will appear.



Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Mon, Dec 14, 2015 at 10:07 AM, Bob Selcoe <rselcoe at entouchonline.net>
wrote:

> Hi Eric an Seqfans,
>
> 9 does not appear.
>
> Cheers,
> Bob Selcoe
>
> --------------------------------------------------
> From: "Eric Angelini" <Eric.Angelini at kntv.be>
> Sent: Monday, December 14, 2015 8:59 AM
> To: "Sequence Fanatics" <seqfan at list.seqfan.eu>
> Cc: <alexandre.wajnberg at skynet.be>
> Subject: [seqfan] Fractions, digits, decimal expansion
>
>
> Hello SeqFans,
>> Here is an echo to the seq computed by Hans Havermann last July:
>> https://oeis.org/A257664
>>
>> a(1)=1; a(n+1) is the smallest positive integer not yet used
>> such that the set of the different digits present in the
>> fraction F=a(n)/a(n+1) is visible in the decimal expansion of F:
>>
>> S = 1,6,13,10,14,17,7,8,...
>>
>> Example:
>> 1/6 = 0,1666... (we see 1 and 6)
>> 6/13 = 0,461538461538... (we see 6, 1 and 3)
>> 13/10 = 1,30 (yes, we admit this zero)
>> 10/14 = 0,7142857142... (we see 1, 0 and 4)
>> 14/17 = 0,8235294117... (we see 1, 4 and 7)
>> 17/7 = 2,4285714285... (we see 1 and 7)
>> 7/8 = 0,875 (we see 7 and 8)
>> etc.
>>
>> Is S a permutation of the natural numbers > 0?
>>
>> Best,
>> É.
>>
>>
>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>>
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