[seqfan] a.b.c = concatenation of [ab]

Eric Angelini Eric.Angelini at kntv.be
Fri Mar 16 17:59:45 CET 2012


Hello SeqFan,
looking for integers a, b and c such that a.b.c = [ab]
[ab] being the concatenation of a and b.

An S sequence of such [ab]s would include those:

S = 11, 12, 15, 24, 36, 110, 120, 150, 240, 360, ...
a =  1   1   1   2   3    1    1    1    2    3  ...
b =  1   2   5   4   6   10   20   50   40   60  ...
c = 11   6   3   3   2   11    6    3    3    2  ...

Are there [ab] integers escaping the above pattern?

In graphic terms, we are looking for integers 
like ABCDEFGHIJKLM divible by the product, say, 
ABC.DEFGHIJKLM or ABCDEF.GHIJKLM or ABCDEFGHIJKL.M 
or... etc. 
(With ABC = 360 we have ABC divisible by A.BC)

Best,
É.






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