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A205122 Least k such that n divides s(k)-s(j) for some j satisfying 1<=j where s(j)=j*(2^(j-1)).

%I A205122 #5 Mar 30 2012 18:58:10
%S A205122 2,3,2,3,4,5,4,3,6,4,3,5,7,4,6,5,5,6,5,4,10,8,7,5,9,7,11,4,9,6,4,6,8,
%T A205122 5,10,6,7,5,11,6,13,10,16,8,6,7,6,5,9,9,8,7,10,11,13,6,14,9,8,6,16,8,
%U A205122 10,7,17,9,15,5,12,10
%N A205122 Least k such that n divides s(k)-s(j) for some j satisfying 1<=j<k, where s(j)=j*(2^(j-1)).
%C A205122 See A204892 for a discussion and guide to related sequences.
%t A205122 s[n_] := s[n] = n*2^(n - 1); z1 = 250; z2 = 70;
%t A205122 Table[s[n], {n, 1, 30}]   (* A001787 *)
%t A205122 u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]]
%t A205122 Table[u[m], {m, 1, z1}]   (* A205120 *)
%t A205122 v[n_, h_] := v[n, h] = If[IntegerQ[u[h]/n], h, 0]
%t A205122 w[n_] := w[n] = Table[v[n, h], {h, 1, z1}]
%t A205122 d[n_] := d[n] = First[Delete[w[n], Position[w[n], 0]]]
%t A205122 Table[d[n], {n, 1, z2}]   (* A205121 *)
%t A205122 k[n_] := k[n] = Floor[(3 + Sqrt[8 d[n] - 1])/2]
%t A205122 m[n_] := m[n] = Floor[(-1 + Sqrt[8 n - 7])/2]
%t A205122 j[n_] := j[n] = d[n] - m[d[n]] (m[d[n]] + 1)/2
%t A205122 Table[k[n], {n, 1, z2}]            (* A205122 *)
%t A205122 Table[j[n], {n, 1, z2}]            (* A205123 *)
%t A205122 Table[s[k[n]], {n, 1, z2}]         (* A205124 *)
%t A205122 Table[s[j[n]], {n, 1, z2}]         (* A205125 *)
%t A205122 Table[s[k[n]] - s[j[n]], {n, 1, z2}]     (* A205126 *)
%t A205122 Table[(s[k[n]] - s[j[n]])/n, {n, 1, z2}] (* A205127 *)
%Y A205122 Cf. A001787, A204892, A205127.
%K A205122 nonn
%O A205122 1,1
%A A205122 _Clark Kimberling_, Jan 25 2012