A191143 - OEIS

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

%S 1,5,17,21,53,65,69,85,161,197,209,213,257,261,277,341,485,593,629,

%T 641,645,773,785,789,833,837,853,1025,1029,1045,1109,1365,1457,1781,

%U 1889,1925,1937,1941,2321,2357,2369,2373,2501,2513,2517,2561,2565,2581,3077,3089,3093,3137,3141,3157,3329,3333,3349,3413,4097,4101

%N Increasing sequence generated by these rules:  a(1)=1, and if x is in a then 3x+2 and 4x+1 are in a.

%C See A191113.

%H Reinhard Zumkeller, <a href="/A191143/b191143.txt">Table of n, a(n) for n = 1..10000</a>

%t h = 3; i = 2; j = 4; k = 1; f = 1; g = 9;

%t a = Union[Flatten[NestList[{h # + i, j # + k} &, f, g]]]  (* A191143 *)

%t b = (a - 2)/3; c = (a - 1)/4; r = Range[1, 1500];

%t d = Intersection[b, r] (* A191210 *)

%t e = Intersection[c, r] (* A191136 *)

%t m = (a + 1)/2 (* divisibility property *)

%t p = (a + 3)/4 (* divisibility property *)

%o (Haskell)

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

%o a191143 n = a191143_list !! (n-1)

%o a191143_list = f $ singleton 1

%o    where f s = m : (f $ insert (3*m+2) $ insert (4*m+1) s')

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

%o -- _Reinhard Zumkeller_, Jun 01 2011

%Y Cf. A191113.

%K nonn

%O 1,2

%A _Clark Kimberling_, May 28 2011