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%I #7 Feb 04 2015 04:26:15
%S 0,0,0,2,1,2,0,0,0,2,4,2,2,4,2,0,0,0,0,4,2,2,4,2,4,2,4,2,4,2,6,4,2,6,
%T 4,2,8,8,4,2,2,8,8,4,2,0,0,0,0,0,0,0,0,4,2,4,4,2,4,2,4,4,2,2,4,2,0,6,
%U 0,8,0,0,8,6,0,0,4,2
%N Triangle T(n,k) giving 2*p mod n-1, where p = period of sequence k^i (i=0,1,2,...) mod n (n >= 2, 2<=k<=n).
%e 0; 0,0; 2,1,2; 0,0,0,2; ...
%t period[lst_] := Module[{n, i, j}, n = Length[lst]; For[j = 2, j <= n, j++, For[i = 1, i < j, i++, If[lst[[i]] == lst[[j]], Return[{i - 1, j - i}]]]]; Return[{0, 0}]]; T[n_, k_] := Module[{t, p}, t = Table[PowerMod[k, i, n], {i, 0, 2 n}]; p = period[t][[2]]; Mod[2 p, n - 1]]; Table[T[n, k], {n, 2, 13}, {k, 2, n}] // Flatten (* _Jean-François Alcover_, Feb 04 2015 *)
%Y Cf. A057593, A057594.
%K nonn,tabl,nice
%O 2,4
%A _Gottfried Helms_, Oct 05 2000