A190812 Increasing sequence generated by these rules: a(1)=1, and if x is in a then 2x+1 and 3x+2 are in a.

1, 3, 5, 7, 11, 15, 17, 23, 31, 35, 47, 53, 63, 71, 95, 107, 127, 143, 161, 191, 215, 255, 287, 323, 383, 431, 485, 511, 575, 647, 767, 863, 971, 1023, 1151, 1295, 1457, 1535, 1727, 1943, 2047, 2303, 2591, 2915, 3071, 3455, 3887, 4095, 4373, 4607, 5183, 5831, 6143, 6911, 7775, 8191, 8747, 9215, 10367, 11663

Offset: 1

Author

Clark Kimberling, May 20 2011

Keywords

• nonn

Comments

See A190803.

Links

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

Crossrefs

Cf. A190803, A069353, A190812.

Programs

Haskell

import Data.Set (singleton, deleteFindMin, insert)
a190812 n = a190812_list !! (n-1)
a190812_list = f $ singleton 1
   where f s = m : (f $ insert (2*m+1) $ insert (3*m+2) s')
             where (m, s') = deleteFindMin s
-- Reinhard Zumkeller, Jun 01 2011

Mathematica

h = 2; i = 1; j = 3; k = 2; f = 1; g = 20 ;
a = Union[Flatten[NestList[{h # + i, j # + k} &, f, g]]]  (* A190812 *)
b = (a - 1)/2; c = (a - 2)/3; r = Range[1, 30000];
d = Intersection[b, r] (* A069353 *)
e = Intersection[c, r] (* A190812 conjectured *)

Extensions

a(41)=2047 inserted by Reinhard Zumkeller, Jun 01 2011