prog.sf

#!/usr/bin/ruby

# a(n) is the least number k such that 3^k-2 and 3^k+2 are the product of n prime factors counted with multiplicity.
# https://oeis.org/A335799

# Known terms:
#   2, 12, 18, 38, 79, 75, 153, 313

# Lower-bounds:
#   a(12) >= 565

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

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

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

        var v1 = (3**k - 2)
        var v2 = (3**k + 2)

        var f1 = factordb(v1)
        var f2 = factordb(v2)

        var o1 = f1.sum {|p| p.is_prime ? 1 : 2 }
        var o2 = f2.sum {|p| p.is_prime ? 1 : 2 }

        next if (o1 > n)
        next if (o2 > n)

        var c1 = f1.grep{.is_composite}.prod
        var c2 = f2.grep{.is_composite}.prod

        var p1 = f1.grep{.is_prime}
        var p2 = f2.grep{.is_prime}

        c1 >= (p1.max||1 -> next_prime)**(n - p1.len) || next
        c2 >= (p2.max||1 -> next_prime)**(n - p2.len) || next

        if ((bigomega(v1) == n) && (bigomega(v2) == n)) {
            return k
        }
    }
}

#var from = 2

#say a(9, 521)
#say a(10, 368)
#say a(11, 339)
say a(12, 551)

#~ for n in (1..100) {
    #~ say "a(#{n}) = #{a(n, 1)}"
#~ }