A174330 Least positive x such that g^x = x (mod p) for g=A174329(n), where p=prime(n).

3, 2, 7, 10, 5, 4, 2, 6, 28, 16, 4, 10, 8, 36, 28, 43, 45, 2, 53, 16, 35, 18, 45, 24, 50, 36, 106, 62, 97, 23, 2, 75, 41, 72, 139, 149, 112, 27, 100, 51, 180, 117, 26, 159, 52, 66, 190, 195, 196, 180, 30, 143, 97, 209, 141, 65, 66, 251, 219, 254, 160, 151, 36, 29, 232, 223

Offset

3,1

Comments

The number x is called a fixed point of the discrete logarithm with base g. The number of fixed points for each prime p is tabulated in A084793.

Links

Table of n, a(n) for n=3..68.

Mathematica

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

Crossrefs

Sequence in context: A018891 A034423 A193859 * A099329 A182871 A143329

Adjacent sequences: A174327 A174328 A174329 * A174331 A174332 A174333

Keyword

nonn

Author

T. D. Noe, Mar 18 2010

Extensions

Name edited by M. F. Hasler, Apr 20 2024

Status

approved