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Period of A002067 modulo prime(n).
2

%I #12 Jul 30 2022 12:39:04

%S 1,1,8,3,10,24,32,18,22,56,30,72,80,42,23,104,29,120,66,70,144,39,41,

%T 176,192,200,51,53,216,224,63,130,272,69,296,150,312,162,166,344,178,

%U 360,95,384,392,99,105,222,226,456,464,238,480,125,512,131,536,270,552

%N Period of A002067 modulo prime(n).

%F a(n) = A122149(A000040(n)).

%e A002067 modulo 5 is 1, 1, 2, 2, 4, 4, 3, 3, 1, 1, 2, 2, 4, 4, 3, 3, 1, 1, ... with period 8.

%t max = 100; se = Series[InverseErf[2*x/Sqrt[Pi]], {x, 0, 2*max + 1}]; a[n_] := (2 n + 1)!/2^n*Coefficient[se, x, 2*n + 1]; A002067 = Table[a[n], {n, 0, max}]; period[lst_List] := Catch[lg = If[Length[lst] <= 5, 2, 5]; lst1 = lst[[1 ;; lg]]; km = Length[lst] - lg; Do[If[lst1 == lst[[k ;; k + lg - 1]], Throw[k - 1]]; If[k == km, Throw[0]], {k, 2, km}]]; Table[ period[Mod[A002067, Prime[n]] // Reverse] , {n, 1, 15}] (* _Jean-François Alcover_, Dec 17 2012 *)

%Y Cf. A002067, A122149.

%K nonn

%O 1,3

%A _N. J. A. Sloane_, Aug 06 2008

%E a(9)-a(15) from _Jean-François Alcover_, Dec 17 2012

%E More terms from _Jinyuan Wang_, Jul 30 2022