A191121 Increasing sequence generated by these rules: a(1)=1, and if x is in a then 3x-1 and 4x-1 are in a.

1, 2, 3, 5, 7, 8, 11, 14, 19, 20, 23, 27, 31, 32, 41, 43, 55, 56, 59, 68, 75, 79, 80, 91, 92, 95, 107, 122, 123, 127, 128, 163, 164, 167, 171, 176, 203, 219, 223, 224, 235, 236, 239, 271, 272, 275, 284, 299, 315, 319, 320, 363, 365, 367, 368, 379, 380, 383, 427, 487, 488, 491, 500, 507, 511, 512, 527, 608, 651, 655, 656, 667, 668

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, A191166, A191167.

Programs

Haskell

import Data.Set (singleton, deleteFindMin, insert)
a191121 n = a191121_list !! (n-1)
a191121_list = f $ singleton 1
   where f s = m : (f $ insert (3*m-1) $ insert (4*m-1) s')
             where (m, s') = deleteFindMin s
-- Reinhard Zumkeller, Jun 01 2011

Mathematica

h = 3; i = -1; j = 4; k = -1; f = 1; g = 9;
a = Union[Flatten[NestList[{h # + i, j # + k} &, f, g]]]  (* A191121 *)
b = (a + 1)/3; c = (a + 1)/4; r = Range[1, 1500];
d = Intersection[b, r] (* A191166 *)
e = Intersection[c, r] (* A191167 *)