[seqfan] Re: Starting and Ending Digits

f.firoozbakht at sci.ui.ac.ir f.firoozbakht at sci.ui.ac.ir
Thu Jan 29 07:48:06 CET 2009

```> I'm considering submitting (done by hand, so there may be errors):

> a(n+1) is the smallest number not yet in the sequence which contains
> the last digit of a(n):
>
> 1,10,20,30,40,50,60,70,80,90,100,101,11,12,2,
> 21,13,3,31,14,4,41,15,5,51,16,6,61,17,7,71,18,
> 8,81,19,9,91,102,22,23,32,24,42,25,52,26,62,
> 27,72,28,82,29,92,112,120,103,33,34,43,35,53,
> 36,63,37,73,38,83,39,93,113,123,130,104,44,
> 45,54,46,64,47,74,48,84,49,94,114,124,134,
> 140,105,55,56,65,57,75,58,85,59,95,115,125,
> 135,145,150,106,66,67,76,68,86,69,96,116,
> 126,136,146,156,160,107,77,78,87,79,97,117,
> 127,137,147,157,167,170,108,88,89,98,118,
> 128,138,148,158,168,178,180,109,99,119,129,
> 139,149,159,169,179,189,190,110,200,201,
> 111,112,121,113,131,...

Some of the 161 first terms which were written aren't correct.
The Mathematica coding for this sequence is:

a[1]=1;a[n_]:=a[n]=(b=Table[a[k],{k,n-1}];
For[m=1,MemberQ[b,m]||MemberQ[IntegerDigits[m],Mod[a[n-1],10]],m++];m);
Table[a[t],{t,161}]

So the first 161 terms of the sequence are:

1,10,20,30,40,50,60,70,80,90,100,101,11,12,2,
21,13,3,23,31,14,4,24,34,41,15,5,25,35,45,51,
16,6,26,36,46,56,61,17,7,27,37,47,57,67,71,18,
8,28,38,48,58,68,78,81,19,9,29,39,49,59,69,79,
89,91,102,22,32,42,52,62,72,82,92,112,120,103,
33,43,53,63,73,83,93,113,123,130,104,44,54,64,
74,84,94,114,124,134,140,105,55,65,75,85,95,
115,125,135,145,150,106,66,76,86,96,116,126,
136,146,156,160,107,77,87,97,117,127,137,147,
157,167,170,108,88,98,118,128,138,148,158,168,
178,180,109,99,119,129,139,149,59,169,179,189,
190,110,200,201,111,121,122,132,142

Farideh Firoozbakht

Quoting franktaw at netscape.net:

> It appears to me that A125887 is an erroneous version of A076654.  I
> would recommend marking it as "dead" rather than removing it, because
> this is a very easy mistake to make -- I made it myself, then noticed
> the error.  (Alternatively, the definition could be modified to require
> the next term to have more than one digit; but then the initial 1 is an
> anomaly.)
>
> A125886 is similarly erroneous.  In this case, I don't find the correct
> version of the sequence in the database.
>
> Ref:
> http://www.research.att.com/~njas/sequences/?q=id%3AA125887|id%3AA076654|id%3AA125886
>
> -----
> I'm considering submitting (done by hand, so there may be errors):
>
> a(n+1) is the smallest number not yet in the sequence which contains
> the last digit of a(n):
>
> 1,10,20,30,40,50,60,70,80,90,100,101,11,12,2,
> 21,13,3,31,14,4,41,15,5,51,16,6,61,17,7,71,18,
> 8,81,19,9,91,102,22,23,32,24,42,25,52,26,62,
> 27,72,28,82,29,92,112,120,103,33,34,43,35,53,
> 36,63,37,73,38,83,39,93,113,123,130,104,44,
> 45,54,46,64,47,74,48,84,49,94,114,124,134,
> 140,105,55,56,65,57,75,58,85,59,95,115,125,
> 135,145,150,106,66,67,76,68,86,69,96,116,
> 126,136,146,156,160,107,77,78,87,79,97,117,
> 127,137,147,157,167,170,108,88,89,98,118,
> 128,138,148,158,168,178,180,109,99,119,129,
> 139,149,159,169,179,189,190,110,200,201,
> 111,112,121,113,131,...
>
> I'm a bit reluctant to be adding yet another "base" sequence, however.
>
>> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/

----------------------------------------------------------------
University of Isfahan (http://www.ui.ac.ir)

```