A174329 Least primitive root g such that there exists an x with g^x = x (mod p), where p=prime(n).

2, 3, 2, 2, 3, 13, 5, 2, 17, 17, 11, 3, 5, 2, 40, 2, 32, 59, 5, 3, 2, 3, 5, 8, 35, 2, 6, 3, 3, 2, 106, 2, 2, 6, 142, 42, 5, 8, 2, 2, 19, 5, 2, 3, 92, 3, 2, 6, 27, 7, 7, 6, 131, 5, 2, 6, 5, 3, 243, 2, 5, 17, 10, 2, 201, 10, 2, 2, 3, 7, 6, 32, 153, 125, 2, 5, 3, 236, 8, 2, 343, 14, 15, 2, 3

Offset

3,1

Comments

The number x is called a fixed point of the discrete logarithm with base g. The least x is in A174330. See A174407 for the number of primitive roots that have a fixed point. The number of fixed points for each prime p is tabulated in A084793. Levin and Pomerance prove that a fixed point exists for some primitive root g of p.

References

Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004, Section F9.

Links

Table of n, a(n) for n=3..87.

Mariana Levin and Carl Pomerance, Fixed points for discrete logarithms (preprint).

M. Levin, C. Pomerance, and K. Soundararajan, Fixed points for discrete logarithms, ANTS IX Proceedings, LNCS 6197 (2010), 6-15.

Mathematica

Table[p=Prime[n]; coprimes=Select[Range[p-1], GCD[ #, p-1] == 1 &]; primRoots = PowerMod[PrimitiveRoot[p], coprimes, p]; Select[primRoots, MemberQ[PowerMod[ #, Range[p-1], p] - Range[p-1], 0] &, 1][[1]], {n, 3, 100}]

Crossrefs

Cf. A084793, A174330, A174407.

Sequence in context: A341651 A017828 A140087 * A295312 A212174 A368713

Adjacent sequences: A174326 A174327 A174328 * A174330 A174331 A174332

Keyword

nonn

Author

T. D. Noe, Mar 18 2010

Status

approved