new file: Math/tower_of_distinct_powers.sf

new file:   Math/tower_of_powers_inverse.sf

Author: trizen

Math/both_truncatable_primes_in_base.sf

@@ -23,14 +23,10 @@
 #  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 digits2num(digits, base) {
-    digits.sum_kv {|k,v| base**k * v }
-}
-
 func is_left_truncatable_prime(digits, base) {
 
     for k in (^digits) {
-        is_prime(digits2num([digits[0..k]], base)) || return false
+        base.digits2num(digits.first(k+1)).is_prime || return false
     }
 
     return true
@@ -59,7 +55,7 @@ func both_truncatable_primes(base) {     # finite sequence for each base
                 .sort
 }
 
-for base in (3..11) {
+for base in (3..15) {
     var a = both_truncatable_primes(base)
     say "There are #{'%3d' % a.len} both-truncatable primes in base #{'%2d' % base} where largest is #{a[-1]}"
 }

Math/esthetic_numbers.sf

@@ -18,10 +18,7 @@ func generate_esthetic(root, upto, callback, b=10) {
 
     var v = root.digits2num(b)
 
-    if (v > upto) {
-        return nil
-    }
-
+    return nil if (v > upto)
     callback(v)
 
     var t = root.head

Math/is_both_truncatable_prime.sf

@@ -25,10 +25,6 @@
 #  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 digits2num(arr, base) {
-    arr.sum_kv {|k,v| base**k * v }
-}
-
 func is_left_truncatable_prime(n, base) {
 
     var digits = n.digits(base)

Math/left_truncatable_primes_in_base.sf

@@ -9,10 +9,6 @@
 #   https://en.wikipedia.org/wiki/Truncatable_prime
 #   https://rosettacode.org/wiki/Find_largest_left_truncatable_prime_in_a_given_base
 
-func digits2num(digits, base) {
-    digits.map_kv {|k,v| base**k * v  }.sum
-}
-
 func generate_from_suffix(p, base) {
 
     var seq = [p]

Math/right_truncatable_primes_in_base.sf

@@ -8,10 +8,6 @@
 #   https://www.youtube.com/watch?v=azL5ehbw_24
 #   https://en.wikipedia.org/wiki/Truncatable_prime
 
-func digits2num(digits, base) {
-    digits.sum_kv {|k,v| base**k * v }
-}
-
 func generate_from_prefix(p, base) {
 
     var seq = [p]

Math/tower_of_distinct_powers.sf

@@ -0,0 +1,53 @@
+#!/usr/bin/ruby
+
+# Daniel "Trizen" Șuteu
+# Date: 05 June 2020
+# https://github.com/trizen
+
+# Find a solution to a^b^c^...^(z^z) = n, for a tower of k distinct powers.
+
+func tower_of_powers(n, k) {
+    gather {
+        k.times {
+            take(n = n.lgrt)
+        }
+    }
+}
+
+var arr = tower_of_powers(2, 10)
+
+with ('a') {|l|
+
+    arr.each {|x|
+        say "#{l++} = #{x}"
+    }
+
+    say "\nResult for a^b^c^...^z:"
+    say arr.flip.reduce{|a,b|
+        b**a
+    }
+
+    arr << arr.last
+    say "\nResult for a^b^c^...^(z^z):"
+    say arr.flip.reduce{|a,b|
+        b**a
+    }
+}
+
+__END__
+a = 1.55961046946236934997038876876500299328488351184
+b = 1.37997039661105766557865852046718024244983839926
+c = 1.28486974908322111138116130550302803396637862332
+d = 1.22670717265797917836276308964722787277231977304
+e = 1.18772296630757250640873514031261013753776638981
+f = 1.1598874880354098360292139394176647261367943972
+g = 1.13907200407942084565168221813587429120796585878
+h = 1.1229478230276636302739154417957596485177010612
+i = 1.1101064783478007292988613612539909225461593927
+j = 1.09964821208918239074785053448745934624006797166
+
+Result for a^b^c^...^z:
+1.99999996313334546345876725053319567243649389716
+
+Result for a^b^c^...^(z^z):
+2

Math/tower_of_powers_inverse.sf

@@ -0,0 +1,38 @@
+#!/usr/bin/ruby
+
+# Daniel "Trizen" Șuteu
+# Date: 05 June 2020
+# https://github.com/trizen
+
+# Find a real solution to x^x^x^...^x = n for a tower of k powers.
+
+func tower_of_powers_inverse(n, k) {  # solution for x^x^...^x = n
+    bsearch_inverse(n, {|v|
+        k.of(v).reduce{|a,b|
+            b**a
+        } <~> n
+    })
+}
+
+func nested_powers_inverse(n, k) {   # solution for ((...)^x)^x = n
+    bsearch_inverse(n, {|v|
+        k.of(v).reduce{|a,b|
+            a**b
+        } <~> n
+    })
+}
+
+# Find x such that x^(x^(x^x)) = 2
+# x =1.4466014324298641745973339875976614806873210422...
+with (tower_of_powers_inverse(2, 4)) {|x|
+    say x
+    assert(x**(x**(x**x))  =~= 2)
+}
+
+# Find x such that ((x^x)^x)^x = 2
+# x = 1.3367097349494955658483777999091512580783714292...
+# Equivalently: x^(x^3) = 2
+with (nested_powers_inverse(2, 4)) {|x|
+    say x
+    assert(((x**x)**x)**x =~= 2)
+}

README.md

@@ -452,6 +452,8 @@ A nice collection of day-to-day Sidef scripts.
     * [System of linear equations](./Math/system_of_linear_equations.sf)
     * [Tangent numbers](./Math/tangent_numbers.sf)
     * [Tonelli shanks algorithm](./Math/tonelli_shanks_algorithm.sf)
+    * [Tower of distinct powers](./Math/tower_of_distinct_powers.sf)
+    * [Tower of powers inverse](./Math/tower_of_powers_inverse.sf)
     * [Towers of hanoi](./Math/towers_of_hanoi.sf)
     * [Trial division with primorials](./Math/trial_division_with_primorials.sf)
     * [Tribonacci closed form](./Math/tribonacci_closed_form.sf)