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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.

%I A191211 #7 Apr 27 2014 00:19:27
%S A191211 1,2,3,5,7,10,11,15,21,23,26,31,43,47,50,53,63,87,95,101,107,122,127,
%T A191211 175,191,203,215,226,245,255,351,383,407,431,442,453,491,511,530,677,
%U A191211 703,767,815,863,885,907,962,983,1023,1061,1355,1407,1535,1631,1727,1771,1815,1850,1925,1967,2047,2123,2210,2501
%N 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.
%C A191211 See A191203.
%H A191211 Reinhard Zumkeller, <a href="/A191211/b191211.txt">Table of n, a(n) for n = 1..10000</a>
%e A191211 1 -> 2,3 -> 5,7,10 ->
%t A191211 g = 11; Union[Flatten[NestList[{1 + 2 #, 1 + #^2} &, 1, g]]]
%t A191211 (* A191211; use g>10 to get all of first 60 terms *)
%o A191211 (Haskell)
%o A191211 import Data.Set (singleton, deleteFindMin, insert)
%o A191211 a191211 n = a191211_list !! (n-1)
%o A191211 a191211_list = f $ singleton 1 where
%o A191211    f s = m : f (insert (2 * m + 1) $ insert (m ^ 2 + 1) s')
%o A191211          where (m, s') = deleteFindMin s
%o A191211 -- _Reinhard Zumkeller_, Apr 18 2014
%Y A191211 Cf. A191203.
%K A191211 nonn
%O A191211 1,2
%A A191211 _Clark Kimberling_, May 29 2011