NEW SEQUENCE: Rotated n,m and n^2,m^2.

[zak seidov]

Subject: NEW SEQUENCE FROM Zak Seidov


%I A000001
%S A000001  
12,21,122,221,1222,2221,4615,5461,12222,22221,122222,222221,402046,640204,603069,960306,869041,904186,1222222,2222221
%N A000001 Pairs of n<m such that m is rotated n and
also m^2 is rotated n^2.
%C A000001 No nore terms <10^9. Inspired by Dawid
Wilson's messages in seqfan list.
%e A000001 12 and 21 are rotationally connected, and
also their squares  144, 441 are obtained from each
other by rotation of their decimal representations.
Also 122 and 221 are rotationally connected as well as
their squares 14884 and 48841.
Notice infinite pattern (n,m)= (12...2, 2...21).
Corresponding squares:
{144,441},
{14884,48841},
{1493284,4932841},
{21298225,29822521},
{149377284,493772841},
{14938217284,49382172841},
{161640986116,409861161616},
{363692218761,922187613636},
{755232259681,817552322596},
{1493826617284,4938266172841}.
%O A000001 1
%K A000001 ,base,more,nonn,
%A A000001 Zak Seidov (zakseidov at yahoo.com), Jan 12
2008

--- zak seidov <zakseidov at yahoo.com> wrote:

> typo correction:
> totated=>rotated
> --- zak seidov <zakseidov at yahoo.com> wrote:
> 
>  Pairs of n<m
>  such that m is rotated n
>  and also m^2 is rotated n^2
>  {12,21},
>  {122,221},
>  {1222,2221},
>  {4615,5461},
>  {12222,22221},
>  {122222,222221},
>  {402046,640204},
>  {603069,960306},
>  {869041,904186},
>  {1222222,2222221}
>  Notice infinite pattern 12...2.
>  Corresponding squares:
> 
>
{{144,441},{14884,48841},{1493284,4932841},{21298225,29822521},{149377284,493772841},{14938217284,49382172841},{161640986116,409861161616},{363692218761,922187613636},{755232259681,817552322596},{1493826617284,4938266172841}}.
>  zak
>  
>  
> > --- Bob Hearn <seqfan at hearn.to> wrote:
> > 
> > > This is a cute pair (but still only a pair):
> > > 
> > > 1222222222^2 =  1493827159950617284,
> > > 2222222221^2 =  4938271599506172841,
> > > 
> > > rotating the result by one place.
> > > 
> > > And here's a solution in base 23:
> > > 
> > > 59L^2 = 16B964,
> > > BL3^2 = 6416B9,
> > > G4B^2 = B96416.
> > > 
> > > Bob
> > > 
> > > 
> > > 
> > > On Jan 9, 2008, at 2:33 PM, David W. Wilson
> wrote:
> > > 
> > > > Let an n-digit number be valid if it does not
> > > start or end with 0.
> > > >
> > > > Let a rotation of n be gotten by rotating its
> > > digits. Thus the  
> > > > rotations of 256 are 256, 562 and 625.
> > > >
> > > > We note that 256 has two valid square
> rotations,
> > > 256 and 625.
> > > >
> > > > Is there a number with more than two valid
> > square
> > > rotations?
> > > 



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