sidef-scripts/Math/is_both_truncatable_prime.sf

#!/usr/bin/ruby

# Daniel "Trizen" Șuteu
# Date: 16 January 2018
# https://github.com/trizen

# Check if a given number is left-truncatable and right-truncatable in a given base.

# Maximum value for each base is given in the following OEIS sequence:
#   https://oeis.org/A323137

# See also:
#   https://www.youtube.com/watch?v=azL5ehbw_24
#   https://en.wikipedia.org/wiki/Truncatable_prime

# Left-truncatable primes in base 10:
#   https://oeis.org/A024785

# Right-truncatable primes in base 10:
#   https://oeis.org/A024770

# Other related sequences:
#  https://oeis.org/A076586 - Total number of right truncatable primes in base n.
#  https://oeis.org/A076623 - Total number of left truncatable primes (without zeros) in base n.
#  https://oeis.org/A323390 - Total number of primes that are both left-truncatable and right-truncatable in base n.
#  https://oeis.org/A323396 - Irregular array read by rows, where T(n, k) is the k-th prime that is both left-truncatable and right-truncatable in base n.

func is_left_truncatable_prime(n, base) {

    var digits = n.digits(base)

    while (digits) {
        digits[-1] || return false
        is_prime(digits2num(digits, base)) || return false
        digits.first!(-1)
    }

    return true
}

func is_right_truncatable_prime(n, base) {

    var digits = n.digits(base)

    while (digits) {
        is_prime(digits2num(digits, base)) || return false
        digits.last!(-1)
    }

    return true
}

func is_both_truncatable(n, base) {
    is_left_truncatable_prime(n, base) &&
    is_right_truncatable_prime(n, base)
}

say is_both_truncatable(21335388527, 30)            #=> true
say is_both_truncatable(1591175082967, 64)          #=> true
say is_both_truncatable(1272571820725769, 42)       #=> true
say is_both_truncatable(200416308070405393, 60)     #=> true

say { is_left_truncatable_prime(_, 10) }.first(20)   #=> [2, 3, 5, 7, 13, 17, 23, 37, 43, 47, 53, 67, 73, 83, 97, 113, 137, 167, 173, 197]
say { is_right_truncatable_prime(_, 10) }.first(20)  #=> [2, 3, 5, 7, 23, 29, 31, 37, 53, 59, 71, 73, 79, 233, 239, 293, 311, 313, 317, 373]