

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.


6



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
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OFFSET

1,2


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.


LINKS

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


EXAMPLE

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


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 *)


CROSSREFS

Cf. A190503, A191100, A191113, A191203.
Sequence in context: A107791 A181518 A262231 * A307207 A165288 A327572
Adjacent sequences: A191320 A191321 A191322 * A191324 A191325 A191326


KEYWORD

nonn


AUTHOR

Clark Kimberling, May 30 2011


STATUS

approved



