A191143 Increasing sequence generated by these rules: a(1)=1, and if x is in a then 3x+2 and 4x+1 are in a.

1, 5, 17, 21, 53, 65, 69, 85, 161, 197, 209, 213, 257, 261, 277, 341, 485, 593, 629, 641, 645, 773, 785, 789, 833, 837, 853, 1025, 1029, 1045, 1109, 1365, 1457, 1781, 1889, 1925, 1937, 1941, 2321, 2357, 2369, 2373, 2501, 2513, 2517, 2561, 2565, 2581, 3077, 3089, 3093, 3137, 3141, 3157, 3329, 3333, 3349, 3413, 4097, 4101

Offset: 1

Author

Clark Kimberling, May 28 2011

Keywords

• nonn

Comments

See A191113.

Links

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

Crossrefs

Cf. A191113.

Programs

Haskell

import Data.Set (singleton, deleteFindMin, insert)
a191143 n = a191143_list !! (n-1)
a191143_list = f $ singleton 1
   where f s = m : (f $ insert (3*m+2) $ insert (4*m+1) s')
             where (m, s') = deleteFindMin s
-- Reinhard Zumkeller, Jun 01 2011

Mathematica

h = 3; i = 2; j = 4; k = 1; f = 1; g = 9;
a = Union[Flatten[NestList[{h # + i, j # + k} &, f, g]]]  (* A191143 *)
b = (a - 2)/3; c = (a - 1)/4; r = Range[1, 1500];
d = Intersection[b, r] (* A191210 *)
e = Intersection[c, r] (* A191136 *)
m = (a + 1)/2 (* divisibility property *)
p = (a + 3)/4 (* divisibility property *)