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

1,2

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

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A002977.

Sequence in context: A003610 A201776 A206476 * A095879 A342751 A120736

Adjacent sequences: A077474 A077475 A077476 * A077478 A077479 A077480

Keyword

easy,nice,nonn

Author

Paul D. Hanna, Nov 08 2002

Status

approved