right_truncatable_primes_in_base.sf

#!/usr/bin/ruby

# Generate right-truncatable primes in a given base.

# See also:
#   https://oeis.org/A076586 -- Total number of right truncatable primes in base n.
#   https://oeis.org/A023107 -- Largest integer in which every prefix is prime in base n (written in base 10).
#   https://www.youtube.com/watch?v=azL5ehbw_24
#   https://en.wikipedia.org/wiki/Truncatable_prime

func generate_from_prefix(p, base, digits) {

    var seq = [p]

    digits.each {|d|
        var num = (base*p + d)
        if (num.is_prime) {
            seq << __FUNC__(num, base, digits)...
        }
    }

    return seq
}

func right_truncatable_primes(base) {       # finite sequence for each base

    var prime_digits = (base-1 -> primes)   # prime digits < base
    var end_digits   = (1 ..^ base -> grep { .is_coprime(base) })

    prime_digits.map  {|p| generate_from_prefix(p, base, end_digits)... }\
                .sort
}

for n in (3..15) {
    var rtp = right_truncatable_primes(n)
    say ("There are #{'%3d' % rtp.len} right-truncatable primes in base #{'%2d' % n}, where largest is #{rtp.max}")
}

__END__
There are   4 right-truncatable primes in base  3, where largest is 71
There are   7 right-truncatable primes in base  4, where largest is 191
There are  14 right-truncatable primes in base  5, where largest is 2437
There are  36 right-truncatable primes in base  6, where largest is 108863
There are  19 right-truncatable primes in base  7, where largest is 6841
There are  68 right-truncatable primes in base  8, where largest is 4497359
There are  68 right-truncatable primes in base  9, where largest is 1355840309
There are  83 right-truncatable primes in base 10, where largest is 73939133
There are  89 right-truncatable primes in base 11, where largest is 6774006887
There are 179 right-truncatable primes in base 12, where largest is 18704078369
There are 176 right-truncatable primes in base 13, where largest is 122311273757
There are 439 right-truncatable primes in base 14, where largest is 6525460043032393259
There are 373 right-truncatable primes in base 15, where largest is 927920056668659