A125138 a(n) = smallest m such that prime(n) divides Sum_{i=1..m} i!, or -1 if no such m exists.

-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

Offset

1,2

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.

References

F. Smarandache, Definitions solved and unsolved problems, conjectures and theorems in number theory and geometry, edited by M. Perez, Xiquan Publishing House, 2000.

Links

Table of n, a(n) for n=1..83.

F. Smarandache, Definitions, Solved and Unsolved Problems, Conjectures, ...

Eric Weisstein's World of Mathematics, Smarandache-Wagstaff Function.

Maple

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) ; end if ; end do ; RETURN(-1) ; end proc: # R. J. Mathar, Mar 14 2007

Crossrefs

Cf. A007489, A056983, A056984, A056985.

Sequence in context: A144389 A136321 A112987 * A021477 A124939 A187800

Adjacent sequences: A125135 A125136 A125137 * A125139 A125140 A125141

Keyword

sign

Author

N. J. A. Sloane, Jan 21 2007

Extensions

More terms from R. J. Mathar, Mar 14 2007

Status

approved