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 Some powers decomposed (Posted on 2015-04-16)
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.

 No Solution Yet Submitted by Ady TZIDON No Rating

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 Thoughts from OEIS | Comment 3 of 5 |
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 2015-04-17 08:52:47

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