A191211 Increasing sequence generated by these rules: a(1)=1, and if x is in a then 1+2x and 1+x^2 are in a.

1, 2, 3, 5, 7, 10, 11, 15, 21, 23, 26, 31, 43, 47, 50, 53, 63, 87, 95, 101, 107, 122, 127, 175, 191, 203, 215, 226, 245, 255, 351, 383, 407, 431, 442, 453, 491, 511, 530, 677, 703, 767, 815, 863, 885, 907, 962, 983, 1023, 1061, 1355, 1407, 1535, 1631, 1727, 1771, 1815, 1850, 1925, 1967, 2047, 2123, 2210, 2501

Offset: 1

Author

Clark Kimberling, May 29 2011

Keywords

• nonn

Comments

See A191203.

Examples

			1 -> 2,3 -> 5,7,10 ->
		

Links

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

Crossrefs

Cf. A191203.

Programs

Haskell

import Data.Set (singleton, deleteFindMin, insert)
a191211 n = a191211_list !! (n-1)
a191211_list = f $ singleton 1 where
   f s = m : f (insert (2 * m + 1) $ insert (m ^ 2 + 1) s')
         where (m, s') = deleteFindMin s
-- Reinhard Zumkeller, Apr 18 2014

Mathematica

g = 11; Union[Flatten[NestList[{1 + 2 #, 1 + #^2} &, 1, g]]]
(* A191211; use g>10 to get all of first 60 terms *)