A051145 a(0)=0, a(1)=1, a(n) = smallest number such that sequence b(n) = a(n) OR a(n+1) is strictly monotonically increasing.

0, 1, 2, 4, 3, 8, 4, 9, 6, 16, 7, 24, 32, 25, 34, 28, 35, 64, 36, 65, 38, 72, 39, 80, 40, 81, 42, 84, 43, 128, 44, 129, 46, 144, 47, 192, 48, 193, 50, 196, 51, 200, 52, 201, 54, 256, 55, 264, 64, 265, 66, 268, 67, 272, 68, 273, 70, 280, 71, 288, 72, 289, 74, 292, 75, 304

Offset

0,3

Comments

a(A051147(n))) = 2^n; A209229(a(A244747(n))) = 1. - Reinhard Zumkeller, Jul 06 2014

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Formula

a(n) = ((a(n-1) OR a(n-2)) + 1) AND NOT a(n-1). - Charlie Neder, Oct 12 2018

Example

To find a(6): we have a(4)=3=11, a(5)=8=1000, 3 OR 8 = 1011 = 11, smallest number which when OR-ed with 8 gives a number bigger than 11 is 4, since then 4=100 OR 8=1000 = 1100=12; so a(6)=4, b(6)=12 (cf. A051146).

Mathematica

a[0] = 0; a[1] = 1; a[n_] := a[n] = (b = 0; While[b++; BitOr[b, a[n-1]] <= BitOr[a[n-2], a[n-1]]]; b); Table[a[n], {n, 0, 65}] (* Jean-François Alcover, Oct 07 2011 *)

Prog

(Haskell)
import Data.Bits ((.|.))
a051145 n = a051145_list !! n
a051145_list = 0 : 1 : f 1 1 where
   f x b = y : f y z where
     (y, z) = head [(y, z) | y <- [1..],
                             let z = x .|. y :: Integer, z > b]
-- Reinhard Zumkeller, Oct 25 2012

Crossrefs

Cf. A051146, A051147, A057923-A057931, A209229, A244747.

Sequence in context: A324213 A052131 A329486 * A288966 A057495 A321366

Adjacent sequences: A051142 A051143 A051144 * A051146 A051147 A051148

Keyword

nonn,easy,nice

Author

N. J. A. Sloane, E. M. Rains

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Oct 03 2000

Status

approved