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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).

%I A054503 #22 Aug 23 2025 18:20:21
%S A054503 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 A054503 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 A054503 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 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).
%D A054503 T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, Table 10.2, pp. 216-217.
%e A054503 Triangle starts:
%e A054503   0;
%e A054503   0,1;
%e A054503   0,1,3,2;
%e A054503   0,2,1,4,5,3;
%e A054503   0,1,8,2,4,9,7,3,6,5;
%e A054503   ...
%t A054503 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 A054503 Columns of table give A054505-A054513.
%K A054503 nonn,tabf,nice,easy,changed
%O A054503 0,6
%A A054503 _N. J. A. Sloane_, Apr 08 2000
%E A054503 More terms from _James Sellers_, Apr 09 2000