Given the sum-of-factorials function

for Prime is the smallest integer such that . The first few known values of are 2, 4, 6, 6, 5, 7, 7, 12, 22, 16, 55, 54, 42, 24, ... for , 5, 7, 11, 17, 19, 23, 31, 37, 41, 61, 71, 73, 89, .... The values for , 13, 29, 43, 47, 53, 67, 79, 83, ..., if they are finite, must be very large (e.g., ).

**References**

Ashbacher, C. ``Some Properties of the Smarandache-Kurepa and Smarandache-Wagstaff Functions.'' *Math. Informatics Quart.*
**7**, 114-116, 1997.

Mudge, M. ``Introducing the Smarandache-Kurepa and Smarandache-Wagstaff Functions.'' *Smarandache Notions J.* **7**, 52-53, 1996.

Mudge, M. ``Introducing the Smarandache-Kurepa and Smarandache-Wagstaff Functions.'' *Abstracts of Papers Presented to the Amer. Math. Soc.*
**17**, 583, 1996.

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1999-05-26