sidef-scripts/Math/generate_primes_with_digits_in_nondecreasing_order.sf

#!/usr/bin/ruby

# Daniel "Trizen" Șuteu
# Date: 15 August 2021
# https://github.com/trizen

# Generate prime numbers that have digits in nondecreasing order.

# See also:
#   https://rosettacode.org/wiki/Primes_with_digits_in_nondecreasing_order

# OEIS sequences:
#   https://oeis.org/A028864 -- Primes with digits in nondecreasing order.
#   https://oeis.org/A345325 -- Number of primes less than 10^n with digits in nondecreasing order.

func primes_with_nondecreasing_digits(upto, base = 10) {

    upto = prev_prime(upto+1)

    var list = []
    var digits = @(1..^base -> flip)

    var end_digits = digits.grep { .is_coprime(base) }
    list << digits.grep { .is_prime && !.is_coprime(base) }...

    for k in (0 .. upto.ilog(base)) {
        digits.combinations_with_repetition(k, {|*a|
            var v = a.digits2num(base)
            end_digits.each {|d|
                var n = (v*base + d)
                next if ((n >= base) && (a[0] > d))
                list << n if (n.is_prime && (n <= upto))
            }
        })
    }

    list.sort
}

say primes_with_nondecreasing_digits(1000)

for k in (1..6) {
    var arr = primes_with_nondecreasing_digits(10**k)
    say "There are #{arr.len} primes with digits in nondecreasing order <= 10^#{k}"
}

__END__
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 37, 47, 59, 67, 79, 89, 113, 127, 137, 139, 149, 157, 167, 179, 199, 223, 227, 229, 233, 239, 257, 269, 277, 337, 347, 349, 359, 367, 379, 389, 449, 457, 467, 479, 499, 557, 569, 577, 599, 677]

There are 4 primes with digits in nondecreasing order <= 10^1
There are 16 primes with digits in nondecreasing order <= 10^2
There are 50 primes with digits in nondecreasing order <= 10^3
There are 132 primes with digits in nondecreasing order <= 10^4
There are 315 primes with digits in nondecreasing order <= 10^5
There are 689 primes with digits in nondecreasing order <= 10^6
There are 1413 primes with digits in nondecreasing order <= 10^7
There are 2636 primes with digits in nondecreasing order <= 10^8
There are 4967 primes with digits in nondecreasing order <= 10^9
There are 8563 primes with digits in nondecreasing order <= 10^10
There are 14481 primes with digits in nondecreasing order <= 10^11
There are 23593 primes with digits in nondecreasing order <= 10^12
There are 37127 primes with digits in nondecreasing order <= 10^13