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A093048 a(n) = n minus exponent of 2 in n, with a(0) = 0.

%I A093048 #22 Jul 08 2022 08:23:10
%S A093048 0,1,1,3,2,5,5,7,5,9,9,11,10,13,13,15,12,17,17,19,18,21,21,23,21,25,
%T A093048 25,27,26,29,29,31,27,33,33,35,34,37,37,39,37,41,41,43,42,45,45,47,44,
%U A093048 49,49,51,50,53,53,55,53,57,57,59,58,61,61,63,58,65,65,67,66,69
%N A093048 a(n) = n minus exponent of 2 in n, with a(0) = 0.
%H A093048 R. J. Mathar, <a href="/A093048/b093048.txt">Table of n, a(n) for n = 0..1000</a>
%F A093048 Recurrence: a(2n) = a(n) + n - 1, a(2n+1) = 2n + 1.
%F A093048 G.f.: Sum_{k>=0} (t*(t^3 + t^2 + 1)/(1 - t^2)^2), with t = x^2^k.
%F A093048 a(n) = Sum_{k=1..n} sign(n mod 2^k). - _Wesley Ivan Hurt_, May 09 2021
%e A093048 G.f. = x + x^2 + 3*x^3 + 2*x^4 +  5*x^5 + 5*x^6 + 7*x^7 + 5*x^8 + 9*x^9 + ... - _Michael Somos_, Jan 25 2020
%p A093048 A093048 := proc(n)
%p A093048     n-A007814(n) ;
%p A093048 end proc: # _R. J. Mathar_, Jul 24 2014
%t A093048 a[ n_] := If[ n == 0, n - IntegerExponent[n, 2]]; (* _Michael Somos_, Jan 25 2020 *)
%o A093048 (PARI) a(n) = if(n<1, 0, if(n%2==0, a(n/2) + n/2 - 1, n))
%o A093048 (PARI) a(n) = n - valuation(n, 2) \\ _Jianing Song_, Oct 24 2018
%o A093048 (Python)
%o A093048 def A093048(n): return n-(~n& n-1).bit_length() if n else 0 # _Chai Wah Wu_, Jul 07 2022
%Y A093048 a(n) = n - A007814(n) = A093049(n) + 1, n > 0.
%Y A093048 a(n) is the exponent of 2 in A002689(n-1), A014070(n), A060690(n), A075101(n).
%Y A093048 See also A084623.
%K A093048 nonn
%O A093048 0,4
%A A093048 _Ralf Stephan_, Mar 16 2004