cp's OEIS Frontend

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

%I A153733 #60 Jul 14 2025 17:50:35
%S A153733 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,
%T A153733 28,14,30,0,32,16,34,8,36,18,38,4,40,20,42,10,44,22,46,2,48,24,50,12,
%U A153733 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
%N A153733 Remove all trailing 1's in the binary representation of n.
%C A153733 a(n) is also the map n -> A065423(n+1) applied A007814(n+1) times. - _Federico Provvedi_, Dec 14 2021
%H A153733 Harvey P. Dale, <a href="/A153733/b153733.txt">Table of n, a(n) for n = 0..1000</a>
%H A153733 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A153733 a(n) = n if n is even, a((n-1)/2) if odd.
%F A153733 a(n)/2 = A025480(n).
%F A153733 a(n) = A000265(n+1) - 1. - _M. F. Hasler_, Mar 16 2018
%F A153733 a(n) = n - A331739(n+1). - _Federico Provvedi_, Dec 21 2021
%p A153733 f:= n -> (n+1)/2^padic:-ordp(n+1,2)-1:
%p A153733 map(f, [$0..100]); # _Robert Israel_, Mar 18 2018
%t A153733 Table[If[EvenQ[n],n,FromDigits[Flatten[Most[Split[IntegerDigits[n,2]]]],2]],{n,0,100}] (* _Harvey P. Dale_, Feb 15 2014 *)
%t A153733 a[n_] := BitShiftRight[n + 1, IntegerExponent[n+1, 2]] - 1; a[Range[0,100]] (* _Federico Provvedi_, Dec 21 2021 *)
%o A153733 (Haskell)
%o A153733 a153733 n = if b == 0 then n else a153733 n'  where (n', b) = divMod n 2
%o A153733 -- _Reinhard Zumkeller_, Jul 22 2014
%o A153733 (PARI) A153733(n)=(n+=1)>>valuation(n,2)-1 \\ most efficient variant: use this. - _M. F. Hasler_, Mar 16 2018
%o A153733 (PARI) {a(n)=while(bittest(n,0),n>>=1);n} \\ for illustration: as long as there's a trailing bit 1, remove it. - _M. F. Hasler_, Mar 16 2018
%o A153733 (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. - _M. F. Hasler_, Mar 16 2018
%o A153733 (Python)
%o A153733 def a(n):
%o A153733     while n&1: n >>= 1
%o A153733     return n
%o A153733 print([a(n) for n in range(100)]) # _Michael S. Branicky_, Dec 18 2021
%o A153733 (Python)
%o A153733 def A153733(n): return n>>(~(n+1)&n).bit_length() # _Chai Wah Wu_, Jul 08 2022
%Y A153733 Cf. A000265, A007814, A007088.
%Y A153733 Cf. A163575.
%Y A153733 Cf. A065423, A331739.
%K A153733 nonn,easy
%O A153733 0,3
%A A153733 _Reinhard Zumkeller_, Dec 31 2008