More digital silliness

[zak seidov]

Pairs of n<m
such that m is rotated n
and also m^2 is totated 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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