project-euler/Yet to solve/838 Not coprime.sf

#!/usr/bin/ruby

# Not coprime
# https://projecteuler.net/problem=838

# Let f(N) be the smallest positive integer that is not coprime to any positive integer n <= N
# whose least significant digit is 3.

# For example f(40) equals to 897 = 3 ⋅ 13 ⋅ 23 since it is not coprime to any of 3, 13, 23, 33.
# By taking the natural logarithm (log to base ) we obtain ln f(40) = ln 897 ≈ 6.799056
# when rounded to six digits after the decimal point.

# You are also given ln f(2800) ≈ 715.019337.

# Runtime: 7.351s

# [2183, 2773]
# [945433, 954803, 955523, 964993, 973543, 975703, 982913, 983933, 985373, 985793, 993403, 995563]

func f(n) {
    var arr = (1..n -> grep{ _%10 == 3})

    var primes = arr.grep{.is_prime}
    var prime_prod = primes.prod

    var t = prime_prod

    var coprime = arr.grep{ .is_coprime(t) }

    #say coprime.group_by{.gpf}
    #say coprime.group_by{.lpf}

    var lpfs = Set(coprime.map{.lpf}.uniq.sort...)
    var w = (coprime - coprime.grep { !lpfs.has(.gpf) })
    lpfs = Set(w.map{.lpf}.uniq.sort...)

    t = lcm(t, lpfs.to_a.lcm)
    t = lcm(arr.grep{ .is_coprime(t) }.map{.gpf}.lcm, t)

    return t
}

say f(40)
say f(2800).log.round(-6)
say f(1e6).log.round(-6)

__END__
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