A191110 Increasing sequence generated by these rules: a(1)=1, and if x is in a then 3x and 3x+2 are in a.

1, 3, 5, 9, 11, 15, 17, 27, 29, 33, 35, 45, 47, 51, 53, 81, 83, 87, 89, 99, 101, 105, 107, 135, 137, 141, 143, 153, 155, 159, 161, 243, 245, 249, 251, 261, 263, 267, 269, 297, 299, 303, 305, 315, 317, 321, 323, 405, 407, 411, 413, 423, 425, 429, 431, 459, 461, 465, 467, 477, 479, 483, 485, 729, 731, 735, 737, 747, 749, 753, 755, 783

Offset: 1

Author

Clark Kimberling, May 26 2011

Keywords

• nonn

Comments

See discussions at A190803, A191106. A191110 has closure properties: the positive integers in (A191110)/3 form A191110, and likewise for (-2+A191110).

Links

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

Crossrefs

Cf. A190803, A191106.

Programs

Mathematica

h = 3; i = 0; j = 3; k = 2; f = 1;  g = 7;
a = Union[Flatten[NestList[{h # + i, j # + k} &, f, g]]]  (* A191110 *)
b = a/3; c = (a - 2)/3; r = Range[0, 900];
d = Intersection[b, r] (* A191110 closure property  *)
e = Intersection[c, r] (* A191110 closure property  *)
Flatten[Nest[{#,3#,3#+2}&/@#&,{1},6]]//Union (* Harvey P. Dale, Sep 30 2019 *)