

A174329


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


2



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
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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 A174704 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.


LINKS

Table of n, a(n) for n=3..87.
Mariana Levin and Carl Pomerance, Fixed points for discrete logarithms (preprint)


MATHEMATICA

Table[p=Prime[n]; coprimes=Select[Range[p1], GCD[ #, p1] == 1 &]; primRoots = PowerMod[PrimitiveRoot[p], coprimes, p]; Select[primRoots, MemberQ[PowerMod[ #, Range[p1], p]  Range[p1], 0] &, 1][[1]], {n, 3, 100}]


CROSSREFS

Sequence in context: A341651 A017828 A140087 * A295312 A212174 A160558
Adjacent sequences: A174326 A174327 A174328 * A174330 A174331 A174332


KEYWORD

nonn


AUTHOR

T. D. Noe, Mar 18 2010


STATUS

approved



