prog.sf

#!/usr/bin/ruby

# Exponents d of powers of 2, q, such that each of q-1 and q+1 are either a power of prime or a semiprime.
# https://oeis.org/A345899

# Known terms:
#   1, 2, 3, 4, 5, 7, 11, 13, 17, 19, 23, 31, 61, 101, 127, 167, 199, 347

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

for k in (1..1e6) {

    var check = {|f|
        if (is_prime_power(f.prod)) {
            # prime power -- ok
        }
        else {

            if (f.len == 2) {    # semiprime
                f.all { .is_prime } || next
            }

            f.len > 2 && next
        }
    }

    var a = factordb("2^#{k}-1")
    check(a)

    var b = factordb("2^#{k}+1")
    check(b)

    if (a.all { .is_prime } && b.all { .is_prime }) {
        print(k, ", ")
    }
    else {
        die "\nCan't go beyond #{k}...";
    }
}