World!Of
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WON plate
136 |


[ July 19, 2002 ]
Interesting or not ?

David Brickell (email) 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 numbers reciprocal 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.



A000136 Prime Curios! Prime Puzzle
Wikipedia 136 Le nombre 136














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