tower_of_distinct_powers.sf

#!/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