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

Author

N. J. A. Sloane, Apr 08 2000

Keywords

• nonn
• tabf
• nice
• easy
• changed

Examples

			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;
  ...
		

References

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

Crossrefs

Columns of table give A054505-A054513.

Programs

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 *)

Extensions

More terms from James Sellers, Apr 09 2000