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TASK #1 - Left Factorials
Write a script to compute Left Factorials of 1 to 10. Please refer OEIS
A003422 for more information.
(My summary: left factorial N = sum k! for k in (0..N-1), remembering that
0! = 1! = 1. So lf(N+1) = lf(N) + N!)
Expected Output:
1, 2, 4, 10, 34, 154, 874, 5914, 46234, 409114
MY NOTES: easy, 1 pass, calc N! on the fly (by multiplying (N-1)! by N)
and add (N-1)! to lf(N-1) to give lf(N).
TASK #2 - Factorions
You are given an integer, $n.
Write a script to figure out if the given integer is factorion.
A factorion is a natural number that equals the sum of the factorials of its digits.
Example 1:
Input: $n = 145
Output: 1
Since 1! + 4! + 5! => 1 + 24 + 120 = 145
Example 2:
Input: $n = 123
Output: 0
Since 1! + 2! + 3! => 1 + 2 + 6 <> 123
MY NOTES: cool, precompute 0..9! in a 10 element array, split number into
digits, sum their factorials and check if the result if the number you
first thought of. Let's add a tabulating mode (invoked if --tab given) that
shows, which numbers (1..$n) are factorian. Running this as:
./ch-2.pl -t 1000000
reveals that the only base 10 factorians under 1000000 are:
1, 2, 145, 40585
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