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A125138
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Smarandache-Wagstaff function: a(n) = smallest m such that prime(n) divides Sum_{i=1..m} i!, or -1 if no such m exists.
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4
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-1, 2, -1, -1, 4, -1, 5, -1, 12, 19, -1, 24, 32, 19, -1, 20, -1, -1, 20, -1, 7, 57, -1, -1, 6, 83, -1, 15, 33, -1, 38, 9, -1, 23, 70, 71, 57, 17, -1, 26, -1, -1, 28, -1, -1, 56, 67, -1, -1, 73, -1, 75, -1, 114, 177, 76, -1, 137, -1, 76, 29, 172, 132, 87, 265, -1, 52, 142, 9, 76, -1, 311, -1, 209, 37, 149, 115, 227, -1, 370, -1, 333, -1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| One need only check values of m < prime(n).
This takes values -1 at A056985 and values given in A056984 at the primes listed in A056983.
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REFERENCES
| F. Smarandache, Definitions solved and unsolved problems, conjectures and theorems in number theory and geometry, edited by M. Perez, Xiquan Publishing House, 2000.
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LINKS
| F. Smarandache, Definitions, Solved and Unsolved Problems, Conjectures, ...
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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MAPLE
| A007489 := proc(n) add(factorial(k), k=1..n) ; end: A125138 := proc(n) local p, m ; p := ithprime(n) ; for m from 1 to p do if A007489(m) mod p = 0 then RETURN(m) ; fi ; od ; RETURN(-1) ; end: for n from 1 to 120 do printf("%d, ", A125138(n)) ; od ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 14 2007
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CROSSREFS
| Cf. A007489, A056983, A056984, A056985.
Sequence in context: A144389 A136321 A112987 * A021477 A124939 A099020
Adjacent sequences: A125135 A125136 A125137 * A125139 A125140 A125141
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KEYWORD
| sign
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jan 21 2007
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 14 2007
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