A190810 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, 2, 3, 5, 7, 8, 11, 14, 15, 17, 20, 23, 29, 31, 32, 35, 41, 44, 47, 50, 59, 63, 65, 68, 71, 83, 86, 89, 92, 95, 101, 104, 119, 122, 127, 131, 137, 140, 143, 149, 167, 173, 176, 179, 185, 188, 191, 194, 203, 209, 212, 239, 245, 248, 255, 257, 263, 266, 275, 281

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, A190855, A190856.

Programs

Haskell

import Data.Set (singleton, deleteFindMin, insert)
a190810 n = a190810_list !! (n-1)
a190810_list = f $ singleton 1
   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 = 9 ;
a = Union[Flatten[NestList[{h # + i, j # + k} &, f, g]]]  (* A190810 *)
b = (a - 1)/2; c = (a + 1)/3; r = Range[1, 900];
d = Intersection[b, r] (* A190855 *)
e = Intersection[c, r] (* A190856 *)

PARI

is(n)=if(n<7, n!=4, (n%3==1 && is(n\3)) || (n%2 && is(n\2))) \\ Charles R Greathouse IV, Jul 14 2016

Extensions

a(55)=255 inserted by Reinhard Zumkeller, Jun 01 2011