Let f(n) denote the largest prime factor of n which is not a palindrome.

Find all the numbers n (below 20000) such that the sum of the factorials of the digits of n is equal to f(n) reversed.

Example: 2105 = 5*421 and 2!+1!+0!+5! = 124.

My list, formatted as:

n (sum of factorials of digits of n, f(n)):

143 (31, 13)
541 (145, 541)
2105 (124, 421)
2444 (74, 47)
3431 (37, 73)
4144 (73, 37)
4233 (38, 83)
4301 (32, 23)
4440 (73, 37)
10234 (34, 43)
12243 (35, 53)
12341 (34, 43)

Found using a list of primes from the internet and some Excel trickery.

Posted by tomarken on 2014-02-27 15:50:36