# [seqfan] Re: Sharing no digit business

Farideh Firoozbakht f.firoozbakht at sci.ui.ac.ir
Fri Apr 3 17:49:02 CEST 2009

```Hello Alex,

It seems that you have lost some of digits and terms of the sequence.
But according to the table of a(n)-n the first 100 terms that you have
found are the same as the first 100 terms that Paolo has found.

So according to what you have found, a(24)=32 not 25.
Can you explain the reason?

Best wishes,
Farideh

Quoting Alexander Povolotsky <apovolot at gmail.com>:

> Is derivative sequence
>
> b(n) = a(n) - n
>
> of interest too (see below PARI results)
>
>  ?
>
> Cheers
> Alex
>
> gp >
> a(n)=[2,1,4,3,6,5,8,7,10,9,12,3,52,53,49,55,60,57,56,59,58,61,62,63,64,65,65,96,97,99,98,101,102,111,200,103,104,105,106,107,108,110,112,222]
> gp > for(n=1,100,print1("n=",n," a[n]-n=",a[n]-n,"\n"))
> n=1 a[n]-n=1
> n=2 a[n]-n=-1
> n=3 a[n]-n=1
> n=4 a[n]-n=-1
> n=5 a[n]-n=1
> n=6 a[n]-n=-1
> n=7 a[n]-n=1
> n=8 a[n]-n=-1
> n=9 a[n]-n=1
> n=10 a[n]-n=-1
> n=11 a[n]-n=1
> n=12 a[n]-n=18
> n=13 a[n]-n=1
> n=14 a[n]-n=6
> n=15 a[n]-n=1
> n=16 a[n]-n=6
> n=17 a[n]-n=1
> n=18 a[n]-n=5
> n=19 a[n]-n=2
> n=20 a[n]-n=11
> n=21 a[n]-n=12
> n=22 a[n]-n=12
> n=23 a[n]-n=17
> n=24 a[n]-n=8
> n=25 a[n]-n=1
> n=26 a[n]-n=9
> n=27 a[n]-n=1
> n=28 a[n]-n=8
> n=29 a[n]-n=8
> n=30 a[n]-n=-1
> n=31 a[n]-n=11
> n=32 a[n]-n=12
> n=33 a[n]-n=8
> n=34 a[n]-n=16
> n=35 a[n]-n=11
> n=36 a[n]-n=9
> n=37 a[n]-n=11
> n=38 a[n]-n=1
> n=39 a[n]-n=8
> n=40 a[n]-n=11
> n=41 a[n]-n=11
> n=42 a[n]-n=11
> n=43 a[n]-n=6
> n=44 a[n]-n=11
> n=45 a[n]-n=15
> n=46 a[n]-n=11
> n=47 a[n]-n=9
> n=48 a[n]-n=11
> n=49 a[n]-n=9
> n=50 a[n]-n=11
> n=51 a[n]-n=11
> n=52 a[n]-n=11
> n=53 a[n]-n=11
> n=54 a[n]-n=11
> n=55 a[n]-n=11
> n=56 a[n]-n=14
> n=57 a[n]-n=11
> n=58 a[n]-n=9
> n=59 a[n]-n=12
> n=60 a[n]-n=12
> n=61 a[n]-n=12
> n=62 a[n]-n=12
> n=63 a[n]-n=12
> n=64 a[n]-n=13
> n=65 a[n]-n=13
> n=66 a[n]-n=13
> n=67 a[n]-n=13
> n=68 a[n]-n=22
> n=69 a[n]-n=7
> n=70 a[n]-n=11
> n=71 a[n]-n=11
> n=72 a[n]-n=11
> n=73 a[n]-n=11
> n=74 a[n]-n=11
> n=75 a[n]-n=11
> n=76 a[n]-n=12
> n=77 a[n]-n=12
> n=78 a[n]-n=13
> n=79 a[n]-n=21
> n=80 a[n]-n=12
> n=81 a[n]-n=12
> n=82 a[n]-n=12
> n=83 a[n]-n=12
> n=84 a[n]-n=12
> n=85 a[n]-n=12
> n=86 a[n]-n=13
> n=87 a[n]-n=11
> n=88 a[n]-n=13
> n=89 a[n]-n=13
> n=90 a[n]-n=21
> n=91 a[n]-n=109
> n=92 a[n]-n=11
> n=93 a[n]-n=11
> n=94 a[n]-n=11
> n=95 a[n]-n=11
> n=96 a[n]-n=11
> n=97 a[n]-n=11
> n=98 a[n]-n=12
> n=99 a[n]-n=13
> n=100 a[n]-n=122
>
> On Fri, Apr 3, 2009 at 8:48 AM,  <f.firoozbakht at sci.ui.ac.ir> wrote:
>>
>> Hello Paolo,
>>
>>> Up to n=100 (any errors?):
>>> 2,1,4,3,6,5,8,7,10,9,12,30,14,20,16,22,18,23,21,31,33,34,40,32,
>>
>> It seems that a(24)=25 you wrote 32. Am I right?
>>
>> The first 100 terms that you found are:
>>
>>     2,1,4,3,6,5,8,7,10,9,12,30,14,20,16,22,18,23,21,31,33,34,40,32,
>>     26,35,28,36,37,29,42,44,41,50,46,45,48,39,47,51,52,53,49,55,60,
>>     57,56,59,58,61,62,63,64,65,66,70,68,67,71,72,73,74,75,77,78,79,
>>     80,90,76,81,82,83,84,85,86,88,89,91,100,92,93,94,95,96,97,99,98,
>>     101,102,111,200,103,104,105,106,107,108,110,112,222
>>
>> and the first 100 terms that I found are:
>>
>>     2,1,4,3,6,5,8,7,10,9,12,30,14,20,16,22,18,23,21,31,33,34,40,25,
>>     36,27,35,29,37,41,42,38,44,50,46,45,48,47,43,51,52,53,55,56,60,
>>     57,58,59,54,61,62,63,64,66,67,70,68,69,71,72,73,74,75,77,76,78,
>>     80,79,81,82,83,84,85,86,88,89,90,91,100,92,93,94,95,96,97,99,
>>     98,101,102,111,200,103,104,105,106,107,108,110,112,222
>>
>>
>> Best wishes,
>> Farideh
>>
>>
>> Quoting Paolo Lava <ppl at spl.at>:
>>
>>> Hello Eric,
>>>
>>> Up to n=100 (any errors?):
>>>
>>> 2,1,4,3,6,5,8,7,10,9,12,30,14,20,16,22,18,23,21,31,33,34,40,32,
>>> 26,35,28,36,37,29,42,44,41,50,46,45,48,39,47,51,52,53,49,55,60,
>>> 57,56,59,58,61,62,63,64,65,66,70,68,67,71,72,73,74,75,77,78,79,
>>> 80,90,76,81,82,83,84,85,86,88,89,91,100,92,93,94,95,96,97,99,98,
>>> 101,102,111,200,103,104,105,106,107,108,110,112,222
>>>
>>> Terms not present so far: 11,13,15,17,19,24,25,27,38,43,54,69,87.....
>>>
>>> Best regards
>>>
>>> Paolo
>>>
>>> --- Eric.Angelini at kntv.be wrote:
>>>
>>> From: "Eric Angelini" <Eric.Angelini at kntv.be>
>>> To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
>>> Subject: [seqfan]  Sharing no digit business
>>> Date: Thu, 2 Apr 2009 18:34:52 +0200
>>>
>>>
>>> Hello SeqFans,
>>> I'm still in the "Sharing no digit" business... Could
>>> someone please check this seq:
>>>
>>> "a(n) shares no digit with the a(n)th term of the sequence"
>>>
>>> a(1)=2 -- and to extend the seq, always add the smallest
>>>           integer not used so far.
>>>
>>> S = 2,1,4,3,6,5,8,7,10,9,12,30,14,20,16,22,18,23,21,31,33,34,...
>>>
>>> (a nightmare to do by hand)
>>>
>>> Best,
>>> E.
>>>
>>> (terms *not* in S are also of interest: 11,13,15,17,19,...)
>>>
>>> _______________________________________________
>>>
>>> Seqfan Mailing list - http://list.seqfan.eu/
>>>
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>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>> ----------------------------------------------------------------
>> University of Isfahan (http://www.ui.ac.ir)
>>
>>
>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>
>
> _______________________________________________
>
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