A077477 Least positive integers not excluded by the rule that if n is present then 2n+1 and 3n+1 are not allowed.

1, 2, 6, 8, 9, 10, 11, 12, 14, 15, 16, 18, 20, 22, 24, 26, 27, 30, 32, 35, 36, 38, 39, 40, 42, 44, 47, 48, 50, 51, 52, 54, 56, 57, 58, 59, 60, 62, 63, 64, 66, 68, 69, 70, 72, 74, 75, 76, 78, 80, 83, 84, 86, 87, 88, 90, 92, 93, 94, 96

Offset: 1

Author

Paul D. Hanna, Nov 08 2002

Keywords

• easy
• nice
• nonn

Comments

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

With 10000 terms, one gets a(n)/n -> 1.63317... - Jean-François Alcover Dec 11 2012

Examples

			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.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002977.

Programs

Haskell

import Data.List (delete)
a077477 n = a077477_list !! (n-1)
a077477_list = f [1..] where
   f (x:xs) = x : f (delete (2*x + 1) $ delete (3*x + 1) xs)
-- Reinhard Zumkeller, Sep 14 2011

Mathematica

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 *)