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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 (list; graph; refs; listen; history; text; internal format)
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[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

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

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Last modified August 3 14:40 EDT 2021. Contains 346438 sequences. (Running on oeis4.)