champernowne_constant_nth_digit.sf

#!/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]