[seqfan] Re: Sharing no digit business

Fri Apr 3 16:32:02 CEST 2009

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,...)
>>
>> _______________________________________________
>>
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