experimental-projects/oeis-research/Daniel Suteu/Smallest Carmichael number such that gpf(p-1) = prime(n)/upper_bounds_2.sf

#!/usr/bin/ruby

# a(n) is the smallest Carmichael number such that gpf(p-1) = prime(n) for all prime factors p of a(n), or 0 if no such number exists.

# This program efficiently generates upper-bounds for a(n).

func a(n) {
    var p = prime(n)

    for z in (2..100) {

        var arr = []

        for k in (1 .. round(sqrt(2)**z)) {
            var r = (2*k*p + 1)
            if (r.is_prime && (r.dec.gpf == p)) {
                arr << r
            }
        }

        arr.combinations(3, {|*a|
            var C = a.prod
            return C if C.is_carmichael
        })
    }
}

if (ARGV) {
    say a(ARGV[0].to_i)
    return true
}

for n in (1..100) {
    say ("a(10^#{n}) <= ", a(10**n))
}

__END__
a(10^1)  <= 1269295201
a(10^2)  <= 73881755325361
a(10^3)  <= 80450619910537321
a(10^4)  <= 15886037020062115176481
a(10^5)  <= 49794506529815563415921701
a(10^6)  <= 1254931836141826573323167521
a(10^7)  <= 8508919739555013050246491382764321
a(10^8)  <= 1487446982391835231061076260463688369
a(10^9)  <= 1922278110523271693763383700255402020449
a(10^10) <= 139290264728702092696281089762626914038407921