TOPICS
Search

Smarandache-Wagstaff Function


Given the sum-of-factorials function

 Sigma(n)=sum_(k=1)^nk!,

SW(p) is the smallest integer for p prime such that Sigma[SW(p)] is divisible by p. If pSigma(n) for all n<p, then p never divides any sum for all n. Therefore, the values SW(p) do not exist for 2, 5, 7, 13, 19, 31, ... (OEIS A056985).

The function is defined for p=3, 11, 17, 23, 29, 37, 41, 43, 53, 67, 73, 79, 97, ... (OEIS A056983), with corresponding values 2, 4, 5, 12, 19, 24, 32, 19, 20, 20, 20, 7, 57, 6, ... (OEIS A056985).


See also

Factorial, Smarandache Function

Explore with Wolfram|Alpha

References

Ashbacher, C. "Some Properties of the Smarandache-Kurepa and Smarandache-Wagstaff Functions." Math. Informatics Quart. 7, 114-116, 1997."Functions in Number Theory." http://www.gallup.unm.edu/~smarandache/FUNCT1.TXT.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.Sloane, N. J. A. Sequences A056983, A056984, and A056985 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Smarandache-Wagstaff Function

Cite this as:

Weisstein, Eric W. "Smarandache-Wagstaff Function." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Smarandache-WagstaffFunction.html

Subject classifications