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A038572 a(n) = n rotated one binary place to the right.

%I A038572 #34 Jan 23 2023 02:31:18
%S A038572 0,1,1,3,2,6,3,7,4,12,5,13,6,14,7,15,8,24,9,25,10,26,11,27,12,28,13,
%T A038572 29,14,30,15,31,16,48,17,49,18,50,19,51,20,52,21,53,22,54,23,55,24,56,
%U A038572 25,57,26,58,27,59,28,60,29,61,30,62,31,63,32,96,33,97,34,98,35,99,36,100
%N A038572 a(n) = n rotated one binary place to the right.
%C A038572 Iterating a(n), a(a(n)), ... eventually leads to 2^A000120(n) - 1. - _Franklin T. Adams-Watters_, Apr 09 2010
%H A038572 Indranil Ghosh, <a href="/A038572/b038572.txt">Table of n, a(n) for n = 0..20000</a> (first 1024 terms from T. D. Noe)
%F A038572 a(n) = A053645(n) * A000035(n) + A004526(n) = most significant bit(n) * least significant bit(n) + floor(n/2).
%F A038572 a(0)=0, a(1)=1, a(2n) = n, a(2n+1) = 2a(n) + 2a(n+1) - n. - _Ralf Stephan_, Oct 24 2003
%e A038572 For n = 35, 35_10 = 100011_2, which after rotating one binary place to the right becomes 110001. Now, 110001_2 = 49_10. So, a(35) = 49. - _Indranil Ghosh_, Jan 21 2017
%p A038572 A038572 := proc(n)
%p A038572     convert(n,base,2) ;
%p A038572     ListTools[Rotate](%,1) ;
%p A038572     add( op(i,%)*2^(i-1),i=1..nops(%)) ;
%p A038572 end proc: # _R. J. Mathar_, May 20 2016
%t A038572 Table[ FromDigits[ RotateRight[ IntegerDigits[n, 2]], 2], {n, 0, 80}] (* _Robert G. Wilson v_ *)
%o A038572 (Haskell)
%o A038572 a038572 0 = 0
%o A038572 a038572 n = a053645 n * m + n' where (n', m) = divMod n 2
%o A038572 -- _Reinhard Zumkeller_, Dec 03 2012
%o A038572 (PARI) a(n)=if(n<2,return(n)); my(d=binary(n)); fromdigits(concat(d[#d], d[1..#d-1]),2) \\ _Charles R Greathouse IV_, Sep 02 2015
%o A038572 (Python)
%o A038572 def A038572(n):
%o A038572     x = bin(n)[2:]
%o A038572     return int(x[-1]+x[:-1],2) # _Indranil Ghosh_, Jan 21 2017
%o A038572 (Python)
%o A038572 def A038572(n): return (n>>1)+(1<<n.bit_length()-1 if n&1 else 0) # _Chai Wah Wu_, Jan 22 2023
%Y A038572 Cf. A006257, A088146.
%K A038572 easy,base,nonn,nice
%O A038572 0,4
%A A038572 _Marc LeBrun_