A121760/1: two (interesting?) sequences

[Joerg Arndt]

* zak seidov <zakseidov at yahoo.com> [Aug 21. 2006 09:28]:
> Seqfans,
> I've just send two (interesting?) sequences,
> two b-files
> and two relative (nice?) graphs with 1000 points.
> Hope they are of some interest,
> Thanks, Zak

Why not go for base 2 with these base dependent sequences?

>  
> 
> %I A121760
> %S A121760
> 1,2,3,4,5,6,7,8,9,1,11,21,31,41,51,61,71,81,91,20,21,22,23,24,25,26,27,28,29,3,13,23,33,43,53,63,73,83,93
> %N A121760 In decimal number system, take negative
> power of 10 at odd digits of n.
> Sequence gives numerators of result.
> %C A121760 See accompanying  sequence A121761 In
> decimal number system, take negative power of 10 at 
> even digits of n.

Let n be an integer written in decimal base:
 n=d0+d1*10^1+...+d(L-1)*10^(L-1).
Let s(k) = -1^k.
a(n) is the numerator of sum(k=0, L-1, d(k)*10^e(k)).


> %F A121760 If n = sum(d(i)*10^(i-1)), then
> a(n)=sum(d(i)*10^((-1)^(1+d(i))*(i-1))).
> %e A121760 a(12)=21 because 12=1*10^1+2*10^0 and 
> a(12)=numerator[1*10^((-1)^(1)*1)+2*10^((-1)^(0)*0)=1/10+2=21/10]=21.
> %A A121760 Zak Seidov (zakseidov at yahoo.com), Aug 20
> 2006
> 
> 
> %I A121761
> %S A121761 
> 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,1,6,11,16,21,26,31,36,41,46,30,31,32,33,34,35,36,37,38,39,2
> [...]


I guess base 10 hides whatever one could possibly find about the
sequences.  Whether the sequences are interesting would more likely
show in base 2.

In such cases one should IMHO discuss on seqfan before submitting.