|
%I #10 Jul 13 2013 12:04:09
%S 1,5,13,21,37,53,61,85,109,149,157,181,213,245,253,325,341,437,445,
%T 469,541,597,629,637,725,733,757,853,973,981,1013,1021,1301,1309,1333,
%U 1365,1405,1621,1749,1781,1789,1877,1885,1909,2165,2173,2197,2269,2389,2517,2549,2557,2901,2917,2933,2941,3029,3037,3061,3413
%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="/A191116/b191116.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]]] (* A191116 *)
%t b = (a + 2)/3; c = (a - 1)/4; r = Range[1, 1500];
%t d = Intersection[b, r] (* A191155 *)
%t e = Intersection[c, r] (* A191129 *)
%t m = (a + 1)/2 (* divisibility property *)
%t p = (a + 3)/4 (* divisibility property *)
%t q = (a + 3)/8 (* divisibility property *)
%o (Haskell)
%o import Data.Set (singleton, deleteFindMin, insert)
%o a191116 n = a191116_list !! (n-1)
%o a191116_list = 1 : f (singleton 5)
%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 27 2011
|
