cp's OEIS Frontend

A204979 Least k such that n divides 2^(k-1)-2^(j-1) for some j satisfying 1<=j

%I A204979 #9 Mar 30 2012 18:58:08
%S A204979 2,3,3,4,5,4,4,5,7,6,11,5,13,5,5,6,9,8,19,7,7,12,12,6,21,14,19,6,29,6,
%T A204979 6,7,11,10,13,9,37,20,13,8,21,8,15,13,13,13,24,7,22,22
%N A204979 Least k such that n divides 2^(k-1)-2^(j-1) for some j satisfying 1<=j<k.
%C A204979 See A204892 for a discussion and guide to related sequences.
%e A204979 1 divides 2^2-2^1, so a(1)=2
%e A204979 2 divides 2^3-2^2, so a(2)=3
%e A204979 3 divides 2^3-2^1, so a(3)=3
%e A204979 4 divides 2^4-2^3, so a(4)=4
%t A204979 s[n_] := s[n] = 2^(n - 1); z1 = 800; z2 = 50;
%t A204979 Table[s[n], {n, 1, 30}]       (* A000079 *)
%t A204979 u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]]
%t A204979 Table[u[m], {m, 1, z1}]       (* A130328 *)
%t A204979 v[n_, h_] := v[n, h] = If[IntegerQ[u[h]/n], h, 0]
%t A204979 w[n_] := w[n] = Table[v[n, h], {h, 1, z1}]
%t A204979 d[n_] := d[n] = First[Delete[w[n], Position[w[n], 0]]]
%t A204979 Table[d[n], {n, 1, z2}]       (* A204939 *)
%t A204979 k[n_] := k[n] = Floor[(3 + Sqrt[8 d[n] - 1])/2]
%t A204979 m[n_] := m[n] = Floor[(-1 + Sqrt[8 n - 7])/2]
%t A204979 j[n_] := j[n] = d[n] - m[d[n]] (m[d[n]] + 1)/2
%t A204979 Table[k[n], {n, 1, z2}]       (* A204979 *)
%t A204979 Table[j[n], {n, 1, z2}]       (* A001511 ? *)
%t A204979 Table[s[k[n]], {n, 1, z2}]    (* A204981 *)
%t A204979 Table[s[j[n]], {n, 1, z2}]    (* A006519 ? *)
%t A204979 Table[s[k[n]] - s[j[n]], {n, 1, z2}]     (* A204983 *)
%t A204979 Table[(s[k[n]] - s[j[n]])/n, {n, 1, z2}] (* A204984 *)
%Y A204979 Cf. A000079, A204892.
%K A204979 nonn
%O A204979 1,1
%A A204979 _Clark Kimberling_, Jan 21 2012