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The intriguing number 1/998001: exploration and visualization

Posted 2 years ago
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Posted 2 years ago
 This post was interesting enough to make me delurk and offer a few comments.First, using N is not really necessary here; RealDigits is smart enough to handle rational numbers with repeating decimal representations: Short[rd = RealDigits[1/998001]] {{{1, 0, 0, 2, 0, 0, 3, 0, 0, 4, 0, 0, 5, 0, 0, 6, 0, 0, 7, 0, 0, 8, 0, 0, 9, 0, 1, 0, 0, 1, 1, 0, 1, 2, 0, 1, 3, 0, 1, 4, 0, 1, 5, 0, 1, 6, 0, 1, 7, 0, 1, 8, 0, 1, 9, 0, 2, 0, 0, 2, 1, <<2876>>, 0, 9, 8, 1, 9, 8, 2, 9, 8, 3, 9, 8, 4, 9, 8, 5, 9, 8, 6, 9, 8, 7, 9, 8, 8, 9, 8, 9, 9, 9, 0, 9, 9, 1, 9, 9, 2, 9, 9, 3, 9, 9, 4, 9, 9, 5, 9, 9, 6, 9, 9, 7, 9, 9, 9, 0, 0, 0, 0, 0}}, <<1>>} rd[[2]] -5 which signifies that the decimal form starts out as 0.00000100200… (five zero digits after the decimal point, and before the first non-zero digit).For convenience, I'll rotate the digits: rdrot = RotateRight[rd[[1, 1]], 4]; for a more convenient representation: FromDigits @ {{rdrot}, -1} 1/998001 Note that Length[rdrot] 2997 which is a multiple of 3, Divisible[%, 3] True and this length can be computed like so: MultiplicativeOrder[10, 998001] 2997
Posted 2 years ago
 Thanks for your hints J. M.
Posted 2 years ago
 Very nice! The next assignment could be: https://twitter.com/potetoichiro/status/1418452296476684288
Posted 2 years ago
 Uau, this is interesting! :-) Adding it to my postits for future investigation...Thanks for the hint!
Posted 2 years ago
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