Factorions
- Definition
A factorion is a natural number that equals the sum of the factorials of its digits. For example 145 is a factorion in base 10 because:
1! + 4! + 5! = 1 + 24 + 120 = 145.
- Task
It can be shown (see Wikipedia article below) that no factorion in base 10 can exceed 1,499,999.
Write a program in your language to demonstrate, by calculating and printing out the factorions, that:
1. There are 4 factorions in base 10.
2. There are 3 factorions in base 9, 5 factorions in base 11 but only 2 factorions in base 12 up to the same upper bound as for base 10.
- See also
C
<lang c>#include <stdio.h>
int main() {
int n, b, d;
unsigned long long i, j, sum, fact[12];
// cache factorials from 0 to 11
fact[0] = 1;
for (n = 1; n < 12; ++n) {
fact[n] = fact[n-1] * n;
}
for (b = 9; b <= 12; ++b) {
printf("The factorions for base %d are:\n", b);
for (i = 1; i < 1500000; ++i) {
sum = 0;
j = i;
while (j > 0) {
d = j % b;
sum += fact[d];
j /= b;
}
if (sum == i) printf("%llu ", i);
}
printf("\n\n");
}
return 0;
}</lang>
- Output:
The factorions for base 9 are: 1 2 41282 The factorions for base 10 are: 1 2 145 40585 The factorions for base 11 are: 1 2 26 48 40472 The factorions for base 12 are: 1 2
Factor
<lang factor>USING: formatting io kernel math math.parser math.ranges memoize prettyprint sequences ; IN: rosetta-code.factorions
! Memoize factorial function MEMO: factorial ( n -- n! ) [ 1 ] [ [1,b] product ] if-zero ;
- factorion? ( n base -- ? )
dupd >base string>digits [ factorial ] map-sum = ;
- show-factorions ( limit base -- )
dup "The factorions for base %d are:\n" printf [ [1,b) ] dip [ dupd factorion? [ pprint bl ] [ drop ] if ] curry each nl ;
1,500,000 9 12 [a,b] [ show-factorions nl ] with each</lang>
- Output:
The factorions for base 9 are: 1 2 41282 The factorions for base 10 are: 1 2 145 40585 The factorions for base 11 are: 1 2 26 48 40472 The factorions for base 12 are: 1 2
Go
<lang go>package main
import (
"fmt" "strconv"
)
func main() {
// cache factorials from 0 to 11
var fact [12]uint64
fact[0] = 1
for n := uint64(1); n < 12; n++ {
fact[n] = fact[n-1] * n
}
for b := 9; b <= 12; b++ {
fmt.Printf("The factorions for base %d are:\n", b)
for i := uint64(1); i < 1500000; i++ {
digits := strconv.FormatUint(i, b)
sum := uint64(0)
for _, digit := range digits {
if digit < 'a' {
sum += fact[digit-'0']
} else {
sum += fact[digit+10-'a']
}
}
if sum == i {
fmt.Printf("%d ", i)
}
}
fmt.Println("\n")
}
}</lang>
- Output:
The factorions for base 9 are: 1 2 41282 The factorions for base 10 are: 1 2 145 40585 The factorions for base 11 are: 1 2 26 48 40472 The factorions for base 12 are: 1 2
OCaml
<lang ocaml>let () =
(* cache factorials from 0 to 11 *) let fact = Array.make 12 0 in fact.(0) <- 1; for n = 1 to pred 12 do fact.(n) <- fact.(n-1) * n; done;
for b = 9 to 12 do
Printf.printf "The factorions for base %d are:\n" b;
for i = 1 to pred 1_500_000 do
let sum = ref 0 in
let j = ref i in
while !j > 0 do
let d = !j mod b in
sum := !sum + fact.(d);
j := !j / b;
done;
if !sum = i then (print_int i; print_string " ")
done;
print_string "\n\n";
done</lang>
Perl 6
<lang perl6>constant @f = 1, |[\*] 1..*;
constant $limit = 1500000;
for 9 .. 12 -> $b {
say "\n\nFactorions in base $b:";
for ^$b { if $_ == @f[$_] { print "$_ " } };
hyper for 1 .. $limit div $b -> $i {
my $sum;
my $prod = $i * $b;
for $i.polymod($b xx *) {
$sum += @f[$_];
$sum = 0 and last if $sum > $prod
}
next if $sum == 0;
print "{$sum + @f[$_]} " and last if $sum + @f[$_] == $prod + $_ for ^$b;
}
}</lang>
- Output:
Factorions in base 9: 1 2 41282 Factorions in base 10: 1 2 145 40585 Factorions in base 11: 1 2 26 48 40472 Factorions in base 12: 1 2
zkl
<lang zkl>var facts=[0..12].pump(List,fcn(n){ (1).reduce(n,fcn(N,n){ N*n },1) }); #(1,1,2,6....) fcn factorions(base){
foreach n in ([1..1_499_999]){
sum,j := 0,n;
while(j>0){
sum+=facts[j%base]; j/=base;
}
if(sum==n) print(" ",n)
}
println();
}</lang> <lang zkl>foreach n in ([9..12]){
print("The factorions for base %2d are: ".fmt(n)); factorions(n);
}</lang>
- Output:
The factorions for base 9 are: 1 2 41282 The factorions for base 10 are: 1 2 145 40585 The factorions for base 11 are: 1 2 26 48 40472 The factorions for base 12 are: 1 2