A244747 -id:A244747 - cp's OEIS frontend

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

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

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

			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).

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

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

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

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 *)

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

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

A051147 Smallest m such that A051145(m) = 2^n.

Original entry on oeis.org

1, 2, 3, 5, 9, 12, 17, 29, 45, 81, 105, 177, 245, 323, 569, 893, 1277, 2121, 3221, 4853, 7697, 11015, 15333, 25841, 40157, 59213, 84239, 135107, 184679, 265277, 445029, 606509, 830411, 1394489, 1973405, 2683997, 4176989, 6710687, 9906153, 15114275, 22269021

Offset: 0

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

Cf. A000079, A051145, subsequence of A244747.

import Data.List (elemIndex); import Data.Maybe (fromJust)
a051147 = fromJust . (`elemIndex` a051145_list) . (2 ^)
-- Reinhard Zumkeller, Jul 05 2014

Block[{a, b, s}, 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); s = Array[a, 2^10, 0]; Array[FirstPosition[s, 2^#][[1]] - 1 &, Floor@ Log2@ Max@ s + 1, 0]] (* Michael De Vlieger, Aug 25 2021, after Jean-François Alcover at A051145 *)

A051145(a(n)) = 2^n. - Reinhard Zumkeller, Jul 05 2014

More terms from Larry Reeves (larryr(AT)acm.org), Oct 03 2000
a(21)-a(23) from Reinhard Zumkeller, Jul 05 2014
Definition corrected by Reinhard Zumkeller, Jul 05 2014
a(24)-a(30) from Charlie Neder, Oct 12 2018
More terms from Sean A. Irvine, Aug 25 2021

cp's OEIS Frontend

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.

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