A057594 Triangle T(n,k) giving floor( (2*p mod n-1)/2), where p = period of sequence k^i (i=0,1,2,...) mod n (n >= 2, 2<=k<=n).

0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 2, 1, 1, 2, 1, 0, 0, 0, 0, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 3, 2, 1, 3, 2, 1, 4, 4, 2, 1, 1, 4, 4, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 0, 3, 0, 4, 0, 0, 4, 3, 0, 0, 2, 1

Offset: 2

Author

Gottfried Helms, Oct 05 2000

Keywords

• nonn
• tabl

Crossrefs

Cf. A057593, A057595.

Programs

Mathematica

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]]; Floor[Mod[2 p, n - 1]/2]]; Table[T[n, k], {n, 2, 13}, {k, 2, n}] // Flatten (* Jean-François Alcover, Feb 04 2015 *)