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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.

%I A191323 #21 May 17 2018 17:24:13
%S A191323 1,2,4,7,11,13,17,20,22,26,31,34,40,47,52,61,67,71,79,92,94,101,103,
%T A191323 107,119,121,139,142,152,155,157,161,179,182,184,202,209,214,229,233,
%U A191323 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
%N 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.
%C A191323 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 [ ].
%C A191323 A191323:  [3x/2]+1, 3x+1
%C A191323 A191324:  [3x/2]+1, 3x+2
%C A191323 A191325:  [3x/2], [5x/2]
%C A191323 A191326:  [3x/2], [7x/2]
%C A191323 A191327:  [5x/2], [7x/2]
%C A191323 A191328:  [5x/3], [7x/3]
%C A191323 Other families of sequences generated by "rules" are listed at A191803, A191106, A101113 and A191203.
%H A191323 Ivan Neretin, <a href="/A191323/b191323.txt">Table of n, a(n) for n = 1..10000</a>
%e A191323 1 -> 2,4 -> 6,7,13 -> 10,11,19,20,22,40 -> ...
%t A191323 h = 3; i = 1; j = 3; k = 1; f = 1; g = 12;
%t A191323 a=Union[Flatten[NestList[{Floor[h#/2]+i,j#+k}&,f,g]]]
%t A191323 (* A191323 *)
%Y A191323 Cf. A190503, A191100, A191113, A191203.
%K A191323 nonn
%O A191323 1,2
%A A191323 _Clark Kimberling_, May 30 2011