Duffin's Sequence for Pi

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Duffin's sequence for positive number is defined by:

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,

where is the integer part of (or the floor of ). For a given , is a sequence of digits 0, 1, 2, ..., 6.

If , we get 0123456012345601234560123456…. Does this sequence have period 0123456?

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Contributed by: Izidor Hafner (August 2016)
Open content licensed under CC BY-NC-SA


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References

[1] R. J. Duffin, "The Patron Saint of Mathematics," The Mathematical Intelligencer, 15(1), 1993 p. 52. doi:10.1007/BF03025258.

[2] I. Vidav, On Division with Remainder and More (in Slovenian), Ljubljana: DMFA, 2016 pp. 85–86.



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