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

Author

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

Keywords

• nonn
• easy
• nice

Comments

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

Examples

			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).
		

Links

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

Crossrefs

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

Programs

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

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 *)

Formula

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

Extensions

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