A191145 Increasing sequence S generated by these rules: a(1)=1, and if x is in S then both 3x+2 and 4x+3 are in S.

1, 5, 7, 17, 23, 31, 53, 71, 95, 127, 161, 215, 287, 383, 485, 511, 647, 863, 1151, 1457, 1535, 1943, 2047, 2591, 3455, 4373, 4607, 5831, 6143, 7775, 8191, 10367, 13121, 13823, 17495, 18431, 23327, 24575, 31103, 32767, 39365, 41471, 52487, 55295, 69983, 73727, 93311, 98303, 118097, 124415, 131071, 157463, 165887

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

See A191113.

Programs

Haskell

import Data.Set (singleton, deleteFindMin, insert)
a191145 n = a191145_list !! (n-1)
a191145_list = f $ singleton 1
   where f s = m : (f $ insert (3*m+2) $ insert (4*m+3) s')
             where (m, s') = deleteFindMin s
-- Reinhard Zumkeller, Jun 01 2011

Mathematica

h = 3; i = 2; j = 4; k = 3; f = 1; g = 11;
a = Union[Flatten[NestList[{h # + i, j # + k} &, f, g]]]  (* A191145 *)
b = (a - 2)/3; c = (a - 3)/4; r = Range[1, 16000];
d = Intersection[b, r] (* A191145 *)
e = Intersection[c, r] (* A191145 *)
m = (a + 1)/2  (* A025613 *)