

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.


7



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
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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(n1) OR a(n2)) + 1) AND NOT a(n1).  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 ORed 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[n1]] <= BitOr[a[n2], a[n1]]]; b); Table[a[n], {n, 0, 65}] (* JeanFrançois 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, A057923A057931, 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



