A190806 - OEIS

%I #11 Jul 13 2013 12:04:09

%S 1,5,9,17,29,33,53,57,65,89,101,105,113,129,161,173,177,197,201,209,

%T 225,257,269,305,317,321,341,345,353,389,393,401,417,449,485,513,521,

%U 533,537,593,605,609,629,633,641,677,681,689,705,773,777,785,801,809,833,897,917,953,965,969

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

%C See A190803.

%H Reinhard Zumkeller, <a href="/A190806/b190806.txt">Table of n, a(n) for n = 1..10000</a>

%t h = 2; i = -1; j = 3; k = 2; f = 1; g = 12 ;

%t a = Union[Flatten[NestList[{h # + i, j # + k} &, f, g]]]  (* A190806 *)

%t b = (a + 1)/2; c = (a - 2)/3; r = Range[1, 1200];

%t d = Intersection[b, r] (* A190804 conjectured *)

%t e = Intersection[c, r] (* A190848 *)

%o (Haskell)

%o import Data.Set (singleton, deleteFindMin, insert)

%o a190806 n = a190806_list !! (n-1)

%o a190806_list = 1 : f (singleton 5)

%o    where f s = m : (f $ insert (2*m-1) $ insert (3*m+2) s')

%o              where (m, s') = deleteFindMin s

%o -- _Reinhard Zumkeller_, Jun 01 2011

%Y Cf. A190803, A190848.

%K nonn

%O 1,2

%A _Clark Kimberling_, May 20 2011

%E a(56)=897 inserted by _Reinhard Zumkeller_, Jun 01 2011