%I #19 Jul 13 2013 16:34:32

%S 1,2,6,8,9,10,11,12,14,15,16,18,20,22,24,26,27,30,32,35,36,38,39,40,

%T 42,44,47,48,50,51,52,54,56,57,58,59,60,62,63,64,66,68,69,70,72,74,75,

%U 76,78,80,83,84,86,87,88,90,92,93,94,96

%N Least positive integers not excluded by the rule that if n is present then 2n+1 and 3n+1 are not allowed.

%C What is the limit of a(n)/n?

%C With 10000 terms, one gets a(n)/n -> 1.63317... - _Jean-François Alcover_ Dec 11 2012

%H Reinhard Zumkeller, <a href="/A077477/b077477.txt">Table of n, a(n) for n = 1..10000</a>

%e a(5)=9 since 9 is not equal to 2*a(k)+1 nor 3*a(k)+1 for 1<=k<5; and since 9 is allowed to be present, then 19(=2*9+1) and 28(=3*9+1) are to be excluded.

%t s = {1}; Do[u = Union[s, 2s + 1, 3s + 1]; c = Complement[Range[u // Last], u] // First; AppendTo[s, c], {10000}]; s (* _Jean-François Alcover_, Dec 11 2012 *)

%o (Haskell)

%o import Data.List (delete)

%o a077477 n = a077477_list !! (n-1)

%o a077477_list = f [1..] where

%o f (x:xs) = x : f (delete (2*x + 1) $ delete (3*x + 1) xs)

%o -- _Reinhard Zumkeller_, Sep 14 2011

%Y Cf. A002977.

%K easy,nice,nonn

%O 1,2

%A _Paul D. Hanna_, Nov 08 2002