upper_bounds.sf

#!/usr/bin/ruby

# a(n) is the smallest number > 1 that is not divisible by 10 but is divisible by the n-th power of the sum of its digits.
# https://oeis.org/A352742

# Computes upper-bounds to a(n).

# Some upper-bounds:
#   a(17) <= 4372327021734283642004853327592915343 = 143^17
#   a(18) <= 15006332672024005536716305894184270692352 = 8 * 152^18
#   a(19) <= 413335079574020313162122296733856201171875 = 155^19
#   a(20) <= 1304064064842535101452541010111722167344300032 = 1282 * 126^20

func a(n, m_limit = 1e4, k_limit = 300) {
    var upper_bound = Inf

    for m in (1..m_limit), k in (2..k_limit) {
        var v = (m * k**n)

        10 `divides` v && next
        v.sumdigits == k || next

        if (v < upper_bound) {
            say "Found: a(#{n}) <= #{v} = #{m} * #{k}^#{n}"
            upper_bound = v
        }
    }

    return upper_bound
}

say a(18, 1e4, 152)
#say a(20, 1e4, 126)