prog_simple.sf

#!/usr/bin/ruby

# Least number k such that k^n and k^n-1 contain the same number of prime factors (counted with multiplicity) or 0 if no such k exists.
# https://oeis.org/A241793

# Known terms:
#   3, 34, 5, 15, 17, 55, 79, 5, 53, 23, 337, 13, 601, 79, 241, 41, 18433, 31, 40961, 89, 3313, 1153

# Lower-bounds:
#   a(23) > 170369

include("../../../factordb/auto.sf")

func a(m, from=2) {
    for k in (from..Inf) {

        var n = bigomega(k)*m
        var v = (k**m - 1)

        say "[#{k}] Checking: #{v}"

        if (k.is_prime && (v.len > 60)) {
            say ":: Checking factordb..."
            var f = try { FF_factordb(v) }
            if (defined(f)) {
                say ":: Success..."
                if (f.len == n) {
                    return k
                }
                else {
                    next
                }
            }
            else {
                say ":: Fail..."
            }
        }

        v.is_almost_prime(n) || next
        return k
    }
}

var from = 157668

for n in (23) {
    say "a(#{n}) = #{a(n, from)}"
}