A191131 Increasing sequence generated by these rules: a(1)=1, and if x is in a then 3x and 4x+3 are in a.

1, 3, 7, 9, 15, 21, 27, 31, 39, 45, 63, 81, 87, 93, 111, 117, 127, 135, 159, 183, 189, 243, 255, 261, 279, 327, 333, 351, 375, 381, 405, 447, 471, 477, 511, 543, 549, 567, 639, 729, 735, 759, 765, 783, 837, 975, 981, 999, 1023, 1047, 1053, 1119, 1125, 1143, 1215, 1311, 1335, 1341, 1407, 1413, 1431, 1503, 1527, 1533, 1623

Offset: 1

Author

Clark Kimberling, May 27 2011

Keywords

• nonn

Comments

See A191113.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A191113, A191186, A191187.

Note that A191131, A261524, A261871, and A282572 are very similar and easily confused with each other.

Programs

Haskell

import Data.Set (singleton, deleteFindMin, insert)
a191131 n = a191131_list !! (n-1)
a191131_list = f $ singleton 1
   where f s = m : (f $ insert (3*m) $ insert (4*m+3) s')
             where (m, s') = deleteFindMin s
-- Reinhard Zumkeller, Jun 01 2011

Mathematica

h = 3; i = 0; j = 4; k = 3; f = 1; g = 9;
a = Union[Flatten[NestList[{h # + i, j # + k} &, f, g]]]   (* A191131 *)
b = a/3; c = (a - 3)/4; r = Range[1, 1500];
d = Intersection[b, r] (* A191186 *)
e = Intersection[c, r] (* A191187 *)