A190805 Increasing sequence generated by these rules: a(1)=1, and if x is in a then 2x-1 and 3x+1 are in a.

1, 4, 7, 13, 22, 25, 40, 43, 49, 67, 76, 79, 85, 97, 121, 130, 133, 148, 151, 157, 169, 193, 202, 229, 238, 241, 256, 259, 265, 292, 295, 301, 313, 337, 364, 385, 391, 400, 403, 445, 454, 457, 472, 475, 481, 508, 511, 517, 529, 580, 583, 589, 601, 607, 625, 673, 688, 715, 724, 727

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, A190845.

Programs

Haskell

import Data.Set (singleton, deleteFindMin, insert)
a190805 n = a190805_list !! (n-1)
a190805_list = 1 : f (singleton 4)
   where f s = m : (f $ insert (2*m-1) $ insert (3*m+1) s')
             where (m, s') = deleteFindMin s
-- Reinhard Zumkeller, Jun 01 2011

Mathematica

h = 2; i = -1; j = 3; k = 1; f = 1; g = 10 ;
a = Union[Flatten[NestList[{h # + i, j # + k} &, f, g]]]  (* A190805 *)
b = (a + 1)/2; c = (a - 1)/3; r = Range[1, 500];
d = Intersection[b, r] (* A190845 *)
e = Intersection[c, r] (* A190808 conjectured *)

Extensions

a(56)=673 inserted by Reinhard Zumkeller, Jun 01 2011