Consider
S1=9 = 1! + 2! + 3!
S2=27 = 1! + 2! + 4!
S3=32 = 2! + 3! + 4!
The S1, S2, S3 represent the values of integer powers that can be represented as a sum of exactly three distinct factorials (0! excluded)
Find S4, S5, S6.
A friendly tip: STOP after S6.
https://oeis.org/A114377 is a slightly different list since it doesn't require
distinct factorials. So it includes e.g. 36 = 3! + 3! + 4!
But it does explain an explanation for the friendly tip: a(11), if it exists, is larger than 10^100.
I think Charlie's idea of stopping at 17! was pretty safe unless he can handle extremely large numbers. The run time doesn't look like much of a barrier, at least to check a little further.
Another variant is https://oeis.org/A082875
which incorrectly notes the only powers are 2 and 3.

Posted by Jer
on 20150417 08:52:47 