[seqfan] Re: Digits concatenation

Paolo Lava paoloplava at gmail.com
Fri Nov 11 13:23:57 CET 2011

```To rearrange the numbers instead of the digits is interesting too, even if
I find more intriguing to mix the digits.

>Consider also those n for which a(n) = 1; i.e., every digit occurs an even
number of times in >1..n. This sequence starts:

>122, 220, 440, 660, 880, 10022, 10100, 10198, 10202, 10918, 11122, 11220,
11440, 11660, ....

That's nice: the sequence of the minimums.

Best

Paolo

2011/11/11 <franktaw at netscape.net>

> We can also consider a variant, to me more natural, where we rearrange the
> numbers 1..n, instead of rearranging the digits of those numbers. This
> doesn't make any difference for n < 10, of course. (It also means you don't
> have to include "leading zeros not permitted" in the definition.)
>
>
>
> -----Original Message-----
> From: Paolo Lava <paoloplava at gmail.com>
>
> Maximilian & Harvey
>
> Yes, you are right. Let us say that I should add to the definition:"...that
> minimize the ratio x/y, being x/y integer and greater than zero (leading
> This sounds good for the sequence starting with a(1)=1 but for the other
>
> Best
>
> Paolo
>
> 2011/11/10 Harvey P. Dale <hpd1 at nyu.edu>
>
>        Indeed, if zero is ever permitted in the numerator all terms
>>
> will
>
>> end up being zero, won't they?
>>        Harvey
>>
>> -----Original Message-----
>> From: maximilian.hasler at gmail.com
>>
> [mailto:maximilian.hasler@**gmail.com <maximilian.hasler at gmail.com>] On
>
>> Behalf Of Maximilian Hasler
>> Sent: Thursday, November 10, 2011 11:12 AM
>> To: paoloplava at gmail.com; Claudio Meller
>> Cc: Harvey P. Dale
>> Subject: Re: [seqfan] Re: Digits concatenation
>>
>> > with 0:
>> >
>> > a(6)= 304/152=2, a(7)= 1046/523=2, a(8)= 10352/647=16, a(9)=
>> > 10476/5328=2
>>
>> But  a(n) = 0/123...n  is a smaller solution, that seems to be valid
>>
> in
>
>> view of your example a(1),
>>
>> >> If we start from a(0)=0 we have a(1)=0 (0/1), a(2)=5 (10/2),
>>
> a(3)=34
>
>>
>> Maximilian
>>
>>
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```