A051147 -id:A051147 - 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

A244747 Positions at which powers of 2 occur in A051145.

Original entry on oeis.org

1, 2, 3, 5, 6, 9, 12, 17, 29, 45, 48, 81, 105, 108, 177, 245, 323, 324, 569, 648, 893, 1277, 1296, 2121, 2592, 3221, 4853, 5184, 7697, 11015, 15333, 15552, 25841, 31104, 40157, 59213, 84239, 93312, 135107, 184679, 265277, 279936, 445029, 606509, 830411, 839808

Offset: 1

Reinhard Zumkeller, Jul 05 2014

nonn

A209229(A051145(a(n))) = 1;

the definition of this sequence was the original definition of A051147.

Rémy Sigrist, C++ program

Cf. A209229, A051147 (subsequence).

import Data.List (findIndices)
a244747 n = a244747_list !! (n-1)
a244747_list = findIndices ((== 1) . a209229) a051145_list
(C++)
See Links section.

More terms from Rémy Sigrist, Oct 09 2022

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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