upper-bounds-faster.sf

#!/usr/bin/ruby

# Smallest overpseudoprime to base 2 (A141232) with n distinct prime factors.
# https://oeis.org/A353409

# Known terms:
#   2047, 13421773, 14073748835533

# Upper-bounds:
#   a(5) <= 1376414970248942474729
#   a(6) <= 48663264978548104646392577273
#   a(7) <= 294413417279041274238472403168164964689
#   a(8) <= 98117433931341406381352476618801951316878459720486433149
#   a(9) <= 1252977736815195675988249271013258909221812482895905512953752551821

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

var n = 7
var psize = 10
var from = 2647
var upto = 3000

say ":: Searching upper-bounds for n = #{n} in range #{from} .. #{upto}"

var min = Hash()

func check_combinations(f,n) {

    var count = 0
    var success = false

    f.combinations(n, {|*a|
        var t = a.prod

        if (t.is_strong_psp) {
            min{n} := Inf
            success = true
            if (t < min{n}) {
                say "\na(#{n}) <= #{t}\n"
                min{n} = t
            }
        }

        break if (++count > 1e6)
    })

    return success
}

var counter = 0

for p in (primes(from, upto)) {

    if (++counter % 10 == 0) {
        say ":: Checking: p = #{p}"
    }

    for k in (p, 4*p, 12*p) {

        var f = factordb(2**k - 1).grep{ .len <= psize }.grep{.is_prime}.grep {|p| powmod(2, k, p) == 1 }.grep{|p| znorder(2,p) == k }

        say "[#{k}] Binomial: #{binomial(f.len, n)}" if (f.len >= n)

        var success = check_combinations(f, n)

        if (success) {
            say ":: Checking also the combinations for n = #{n+1}"
            check_combinations(f, n+1) &&
            check_combinations(f, n+2) &&
            check_combinations(f, n+3) &&
            check_combinations(f, n+4)
        }
    }
}

__END__
a(5) <= 3223802185639011132549803
a(5) <= 636607858967934928371769
a(5) <= 145505063083208835861853
a(5) <= 124250696089090697678753
a(5) <= 79122810072725207031253
a(5) <= 63018455673461680466449
a(5) <= 8278905362357819790631
a(5) <= 1376414970248942474729

a(6) <= 6207602089353930933432401115757211526727413361
a(6) <= 112236525927686091107643454350711622517
a(6) <= 13264566429400773810375679971999741133
a(6) <= 32245825439777493648426550929515449
a(6) <= 721606983841657320586259138751241
a(6) <= 44308853725126158640748255977121
a(6) <= 157839641006967261025228640857
a(6) <= 48663264978548104646392577273

a(7) <= 294413417279041274238472403168164964689

a(8) <= 98117433931341406381352476618801951316878459720486433149

a(9) <= 1252977736815195675988249271013258909221812482895905512953752551821