A054503 Table T(n,k) giving log_b(k), 1<=k<=p, where p = n-th prime and b = smallest primitive root of p (A001918).

0, 0, 1, 0, 1, 3, 2, 0, 2, 1, 4, 5, 3, 0, 1, 8, 2, 4, 9, 7, 3, 6, 5, 0, 1, 4, 2, 9, 5, 11, 3, 8, 10, 7, 6, 0, 14, 1, 12, 5, 15, 11, 10, 2, 3, 7, 13, 4, 9, 6, 8, 0, 1, 13, 2, 16, 14, 6, 3, 8, 17, 12, 15, 5, 7, 11, 4, 10, 9, 0, 2, 16, 4, 1, 18, 19, 6, 10, 3, 9, 20, 14, 21, 17, 8, 7, 12, 15, 5, 13, 11

Offset

0,6

References

T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, Table 10.2, pp. 216-217.

Links

Table of n, a(n) for n=0..90.

Example

Triangle starts:
0;
0,1;
0,1,3,2;
0,2,1,4,5,3;
0,1,8,2,4,9,7,3,6,5;
...

Mathematica

T[n_, k_] := Module[{p, b, lg = 1}, b = PrimitiveRoot[p = Prime[n]]; While[ PowerMod[b, lg, p] != k , lg++]; lg]; T[_, 1] = 0; Table[T[n, k], {n, 1, 10}, {k, 1, Prime[n] - 1}] // Flatten (* Jean-François Alcover, Sep 03 2016 *)

Crossrefs

Columns of table give A054505-A054513.

Sequence in context: A340860 A112606 A108512 * A281451 A246863 A227864

Adjacent sequences: A054500 A054501 A054502 * A054504 A054505 A054506

Keyword

nonn,tabf,nice,easy

Author

N. J. A. Sloane, Apr 08 2000

Extensions

More terms from James A. Sellers, Apr 09 2000

Status

approved