[ July 19, 2002 ]
Interesting pattern in reciprocals
David Brickell (email)

David sent me a short statement
setting my mind into wondering position...

"The reciprocal of any series of the number nine
results in zeros and ones (binary code).
No other number reciprocals does this."

1/9 = 0.1111111111111_
1/99 = 0.0101010101010_
1/999 = 0.0010010010010_
1/9999 = 0.0001000100010_

The pattern is obvious.
but what about these reciprocals :

1/90909 = 0.000011000011_
1/9009009 = 0.000000111000000111_

Indeed a curious observation !
Does anyone has some generalisations in order to
predict or at least confirm these binary outcomes ?

Comments as always are very welcome.