upper-bounds_with_multiplier.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

var K = 19
#var multiplier = 2**K
var multiplier = 3**K

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) {

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

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

        from = upto+1
        upto *= 2
    }
}

upper_bound(6)

__END__

a(17) <= 215189482110975
a(18) <= 766556765683712
a(19) <= 1061522454347775
a(20) <= 19656708706009088
a(21) <= 63530609986764800
a(22) <= 2280241934368767
a(23) <= 1581740688041574399


# Old upper-bounds:

a(17) <= 258756982341632
a(17) <= 350602757668863
a(17) <= 553722671005695
a(17) <= 664996809015296
a(17) <= 2381801891037183
a(18) <= 1985276245704704
a(19) <= 1375916505694208
a(19) <= 5936400374431743
a(20) <= 24217192574746623