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- #!/usr/bin/ruby
- # Compute the nth-digit in the decimal expansion of the Champernowne constant.
- # Formula due to David W. Cantrell (Feb 18 2007)
- # See also:
- # https://oeis.org/A033307
- # https://en.wikipedia.org/wiki/Champernowne_constant
- func champernowne_nth_digit(n) {
- var i = ceil(LambertW(log(10) / 10**(1/9) * (n - 1/9))/log(10) + 1/9)
- floor((10**((n + (10**i - 10)/9) % i - i + 1) * ceil((9*n + 10**i - 1)/(9*i) - 1)) % 10)
- }
- say { champernowne_nth_digit(_) }.map(1..25)
- say { champernowne_nth_digit(_) }.map(19977..20001)
- __END__
- [1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 0, 1, 1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 6, 1, 7]
- [1, 5, 2, 7, 2, 5, 2, 7, 3, 5, 2, 7, 4, 5, 2, 7, 5, 5, 2, 7, 6, 5, 2, 7, 7]
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