login
Monotonic ordering of set S generated by these rules: if x and y are in S then 2xy-x-y is in S, and 2 is in S.
3

%I #5 Mar 30 2012 18:57:34

%S 2,4,10,24,28,66,70,82,164,180,192,196,208,244,446,458,486,490,522,

%T 538,570,574,586,622,730,1104,1144,1244,1256,1292,1320,1336,1340,1368,

%U 1372,1452,1456,1468,1512,1548,1564,1612,1704,1708,1720,1756,1864

%N Monotonic ordering of set S generated by these rules: if x and y are in S then 2xy-x-y is in S, and 2 is in S.

%t start = {2}; f[x_, y_] := 2 x*y - x - y

%t b[x_] :=

%t Block[{w = x},

%t Select[Union[

%t Flatten[AppendTo[w,

%t Table[f[w[[i]], w[[j]]], {i, 1, Length[w]}, {j, 1, i}]]]], # <

%t 5000 &]];

%t t = NestList[b, start, 10][[-1]] (* A192523 *)

%t t/2 (* A192524 *)

%t Table[t[[i]] - t[[i - 1]], {i, 2, Length[t]}] (* differences *)

%Y Cf. A192476.

%K nonn

%O 1,1

%A _Clark Kimberling_, Jul 03 2011