A191323 Increasing sequence generated by these rules: a(1)=1, and if x is in a then [3x/2]+1 and 3x+1 are in a, where [ ]=floor.

1, 2, 4, 7, 11, 13, 17, 20, 22, 26, 31, 34, 40, 47, 52, 61, 67, 71, 79, 92, 94, 101, 103, 107, 119, 121, 139, 142, 152, 155, 157, 161, 179, 182, 184, 202, 209, 214, 229, 233, 236, 238, 242, 269, 274, 277, 283, 304, 310, 314, 322, 344, 350, 355, 358, 364, 404, 412, 416, 418, 425, 427, 457, 466, 472, 484, 517, 526, 533, 538, 547, 553

Offset: 1

Author

Clark Kimberling, May 30 2011

Keywords

• nonn

Comments

This sequence represents a class of sequences generated by rules of the form "a(1)=1, and if x is in a then floor(hx+i) and floor(jx+k) are in a, where h and j are rational numbers and i and k are positive integers." In the following examples, the floor function is denoted by [ ].

A191323: [3x/2]+1, 3x+1

A191324: [3x/2]+1, 3x+2

A191325: [3x/2], [5x/2]

A191326: [3x/2], [7x/2]

A191327: [5x/2], [7x/2]

A191328: [5x/3], [7x/3]

Other families of sequences generated by "rules" are listed at A191803, A191106, A101113 and A191203.

Examples

			1 -> 2,4 -> 6,7,13 -> 10,11,19,20,22,40 -> ...
		

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A190503, A191100, A191113, A191203.

Programs

Mathematica

h = 3; i = 1; j = 3; k = 1; f = 1; g = 12;
a=Union[Flatten[NestList[{Floor[h#/2]+i,j#+k}&,f,g]]]
(* A191323 *)