Digit fifth powers

Digit fifth powers is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Task

Task desciption is taken from Project Eulet(https://projecteuler.net/problem=30)
Find the sum of all the numbers that can be written as the sum of fifth powers of their digits.

Even though 1⁵ = 1, it is not expressed as a sum (a sum being the summation of a list of two or more numbers), and is therefore not included.

Julia

In base 10, the largest digit is 9. If n is the number of digits, as n increases, 9^5 * n < 10^n. So we do not have to look beyond 9^5 * 6 since 9^5 * 6 < 1,000,000. <lang julia>println("Numbers > 1 that can be written as the sum of fifth powers of their digits:") arr = [i for i in 2 : 9^5 * 6 if mapreduce(x -> x^5, +, digits(i)) == i] println(join(arr, " + "), " = ", sum(arr))

</lang>

Output:

Numbers > 1 that can be written as the sum of fifth powers of their digits:
4150 + 4151 + 54748 + 92727 + 93084 + 194979 = 443839

Python

<lang>print(sum([n for n in range(2, 6*9**5) if sum(int(i)**5 for i in str(n)) == n]))</lang>

Output:

443839

Raku

<lang perl6>print q:to/EXPANATION/; Sum of all integers (except 1 for some mysterious reason ¯\_(ツ)_/¯), for which the individual digits to the nth power sum to itself. EXPANATION

sub super($i) { $i.trans('0123456789' => '⁰¹²³⁴⁵⁶⁷⁸⁹') }

for 3..8 -> $power {

   print "\nSum of powers of n{super $power}: ";
   my $threshold = 9**$power * $power;
   put .join(' + '), ' = ', .sum with cache
   (2..$threshold).race.map: {
       state %p = ^10 .map: { $_ => $_ ** $power };
       $_ if %p{.comb}.sum == $_
   }

}</lang>

Output:

Sum of all integers (except 1 for some mysterious reason ¯\_(ツ)_/¯),
for which the individual digits to the nth power sum to itself.

Sum of powers of n³: 153 + 370 + 371 + 407 = 1301

Sum of powers of n⁴: 1634 + 8208 + 9474 = 19316

Sum of powers of n⁵: 4150 + 4151 + 54748 + 92727 + 93084 + 194979 = 443839

Sum of powers of n⁶: 548834 = 548834

Sum of powers of n⁷: 1741725 + 4210818 + 9800817 + 9926315 + 14459929 = 40139604

Sum of powers of n⁸: 24678050 + 24678051 + 88593477 = 137949578

Ring

<lang ring>? "working..."

sumEnd = 0 sumList = ""

pow5 = [] for i = 1 to 9

   add(pow5, pow(i, 5))

next

limitStart = 2 limitEnd = 6 * pow5[9]

for n = limitStart to limitEnd

   sum = 0
   m = n
   while m > 0
       d = m % 10
       if d > 0 sum += pow5[d] ok
       m = unsigned(m, 10, "/")
   end
   if sum = n
      sumList += "" + n + " + "
      sumEnd += n
   ok

next

? "The sum of all the numbers that can be written as the sum of fifth powers of their digits:" ? substr(sumList, 1, len(sumList) - 2) + "= " + sumEnd ? "done..."</lang>

Output:

working...
The sum of all the numbers that can be written as the sum of fifth powers of their digits:
4150 + 4151 + 54748 + 92727 + 93084 + 194979 = 443839
done...

XPL0

Since 1 is not actually a sum, it should not be included. Thus the answer should be 443839. <lang XPL0>\upper bound: 6*9^5 = 354294 \7*9^5 is still only a 6-digit number, so 6 digits are sufficient

int A, B, C, D, E, F, \digits, A=LSD

       A5, B5, C5, D5, E5, F5, \digits to 5th power
       A0, B0, C0, D0, E0, F0, \digits multiplied by their decimal place
       N,              \number that can be written as the sum of its 5th pwrs
       S;              \sum of all numbers

[S:= 0;

for A:= 0, 9 do \for all digits

 [A5:= A*A*A*A*A;
 A0:= A;
 for B:= 0, 9 do
   [B5:= B*B*B*B*B;
   B0:= B*10;
   for C:= 0, 9 do
     [C5:= C*C*C*C*C;
     C0:= C*100;
     for D:= 0, 9 do
       [D5:= D*D*D*D*D;
       D0:= D*1000;
       for E:= 0, 9 do
         [E5:= E*E*E*E*E;
         E0:= E*10000;
         for F:= 0, 3 do
           [F5:= F*F*F*F*F;
           F0:= F*100000;
               [N:= F0 + E0 + D0 + C0 + B0 + A0;
               if N = A5 + B5 + C5 + D5 + E5 + F5 then
                       [S:= S + N;
                       IntOut(0, N);
                       CrLf(0);
                       ];
               ];
           ];
         ];
       ];
     ];
   ];
 ];

CrLf(0); IntOut(0, S); CrLf(0); ]</lang>

Output:

0
4150
1
4151
93084
92727
54748
194979

443840