A054503 - OEIS

%I #11 Sep 03 2016 08:35:50

%S 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,

%T 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,

%U 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

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

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

%e Triangle starts:

%e 0;

%e 0,1;

%e 0,1,3,2;

%e 0,2,1,4,5,3;

%e 0,1,8,2,4,9,7,3,6,5;

%e ...

%t 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 *)

%Y Columns of table give A054505-A054513.

%K nonn,tabf,nice,easy

%O 0,6

%A _N. J. A. Sloane_, Apr 08 2000

%E More terms from _James A. Sellers_, Apr 09 2000