A153733 Remove all trailing 1's in the binary representation of n.

0, 0, 2, 0, 4, 2, 6, 0, 8, 4, 10, 2, 12, 6, 14, 0, 16, 8, 18, 4, 20, 10, 22, 2, 24, 12, 26, 6, 28, 14, 30, 0, 32, 16, 34, 8, 36, 18, 38, 4, 40, 20, 42, 10, 44, 22, 46, 2, 48, 24, 50, 12, 52, 26, 54, 6, 56, 28, 58, 14, 60, 30, 62, 0, 64, 32, 66, 16, 68, 34, 70, 8, 72, 36, 74, 18, 76, 38

Offset

0,3

Comments

a(n) is also the map n -> A065423(n+1) applied A007814(n+1) times. - Federico Provvedi, Dec 14 2021

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for sequences related to binary expansion of n

Formula

a(n) = n if n is even, a((n-1)/2) if odd.

a(n)/2 = A025480(n).

a(n) = A000265(n+1) - 1. - M. F. Hasler, Mar 16 2018

a(n) = n - A331739(n+1). - Federico Provvedi, Dec 21 2021

Maple

f:= n -> (n+1)/2^padic:-ordp(n+1, 2)-1:
map(f, [$0..100]); # Robert Israel, Mar 18 2018

Mathematica

Table[If[EvenQ[n], n, FromDigits[Flatten[Most[Split[IntegerDigits[n, 2]]]], 2]], {n, 0, 100}] (* Harvey P. Dale, Feb 15 2014 *)
a[n_] := BitShiftRight[n + 1, IntegerExponent[n+1, 2]] - 1; a[Range[0, 100]] (* Federico Provvedi, Dec 21 2021 *)

Prog

(Haskell)
a153733 n = if b == 0 then n else a153733 n'  where (n', b) = divMod n 2
-- Reinhard Zumkeller, Jul 22 2014
From  M. F. Hasler, Mar 16 2018: (Start)
(PARI) A153733(n)=(n+=1)>>valuation(n, 2)-1 \\ most efficient variant: use this.
(PARI) {a(n)=while(bittest(n, 0), n>>=1); n} \\ for illustration: as long as there's a trailing bit 1, remove it.
(PARI) a(n)=for(i=0, n, bittest(n, i)||return(n>>i)) \\ scan the trailing 1's, then remove all of them at once. (End)
(Python)
def a(n):
    while n&1: n >>= 1
    return n
print([a(n) for n in range(100)]) # Michael S. Branicky, Dec 18 2021
(Python)
def A153733(n): return n>>(~(n+1)&n).bit_length() # Chai Wah Wu, Jul 08 2022

Crossrefs

Cf. A000265, A007814, A007088.

Cf. A163575.

Cf. A065423, A331739.

Sequence in context: A222303 A097945 A319997 * A083218 A203908 A334082

Adjacent sequences: A153730 A153731 A153732 * A153734 A153735 A153736

Keyword

nonn,easy

Author

Reinhard Zumkeller, Dec 31 2008

Status

approved