A057923 -id:A057923 - cp's OEIS frontend

A057924 Sequence b(n) mentioned in A057923.

2, 3, 5, 6, 7, 13, 14, 15, 25, 26, 27, 29, 30, 31, 45, 46, 47, 49, 50, 51, 53, 54, 55, 61, 62, 63, 89, 90, 91, 93, 94, 95, 125, 126, 127, 225, 226, 227, 229, 230, 231, 237, 238, 239, 249, 250, 251, 253, 254, 255, 397, 398, 399, 401, 402, 403, 405, 406, 407, 413, 414

Offset: 1

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

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A057923, A057925.

A[0]:= 0: A[1]:= 2: B[1]:= 2:
for n from 2 to 100 do
  for k from B[n-1]-A[n-1] do
    b:= Bits:-Or(A[n-1],k);
    if b > B[n-1] then A[n]:= k; B[n]:= b; break fi
  od;
od:
seq(B[n],n=1..100); # Robert Israel, Aug 13 2017

A057925 Position of first occurrence of 2^n in A057923.

Original entry on oeis.org

2, 1, 3, 6, 9, 15, 27, 36, 51, 87, 135, 243, 315, 531, 735, 969, 1707, 2679, 3831, 6363, 9663, 14559, 23091, 33045, 45999, 77523, 120471, 177639, 252717, 405321, 554037, 795831, 1335087, 1819527, 2491233, 4183467, 5920215, 8051991, 12530967

Offset: 0

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

Cf. A057923, A057924.

More terms from David W. Wilson, Jan 11 2001

Definition corrected by Michel Marcus, Aug 02 2013

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.

Original entry on oeis.org

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

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A057924 Sequence b(n) mentioned in A057923.

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A057925 Position of first occurrence of 2^n in A057923.

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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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