upper-bounds.sf

#!/usr/bin/ruby

# a(n) is the least number k such that A046660(k) = A046660(k+1) = n.
# https://oeis.org/A358818

# Known terms:
#   1, 44, 135, 80, 8991, 29888, 123200, 2316032, 1043199, 24151040, 217713663, 689278976, 11573190656, 76876660736, 311969153024, 2035980763136, 2741258240000

func upper_bound(n, from = 2, upto = 2*from) {

    say "\n:: Searching an upper-bound for a(#{n})\n"

    loop {

        var count = n.almost_prime_count(from, upto)

        if (count > 0 && (upto > 2741258240000)) {

            from = max(2741258240000, from)

            say "Sieving range: [#{from}, #{upto}]"
            say "This range contains: #{count.commify} elements\n"

            n.almost_primes_each(from, upto, {|v|
                var t = (n - v.omega)
                if (t >= 17) {
                    var t1 = (v.inc.bigomega - v.inc.omega)
                    if (t == t1) {
                        say "a(#{t}) <= #{v}"
                    }
                    var t2 = (v.dec.bigomega - v.dec.omega)
                    if (t == t2) {
                        say "a(#{t}) <= #{v-1}"
                    }
                }
            })
        }

        from = upto+1
        upto *= 2
    }
}

upper_bound(20)

__END__