Search: id:A048724
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%I A048724
%S A048724 0,3,6,5,12,15,10,9,24,27,30,29,20,23,18,17,48,51,54,53,60,63,58,57,40,
%T A048724 43,46,45,36,39,34,33,96,99,102,101,108,111,106,105,120,123,126,125,
%U A048724 116,119,114,113,80,83,86,85,92,95,90,89,72,75,78,77,68,71,66,65,192
%N A048724 Write n and 2n in binary and add them mod 2.
%C A048724 Reversing binary representation of -n. Converting sum of powers of 2 
               in binary representation of a(n) to alternating sum gives -n. Note 
               that the alternation is applied only to the nonzero bits and does 
               not depend on the exponent of two. All integers have a unique reversing 
               binary representation (see cited exercise for proof). Complement 
               of A065621. - Marc LeBrun (mlb(AT)well.com), Nov 07 2001
%C A048724 A permutation of the "evil" numbers A001969 - Marc LeBrun (mlb(AT)well.com), 
               Nov 07 2001
%C A048724 A048725(n) = a(a(n)). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Nov 12 2004
%D A048724 D. E. Knuth, The Art of Computer Programming. Addison-Wesley, Reading, 
               MA, 1969, Vol. 2, p. 178, (exercise 4.1. Nr. 27)
%H A048724 T. D. Noe, <a href="b048724.txt">Table of n, a(n) for n=0..1023</a>
%H A048724 R. Stephan, <a href="somedcgf.html">Some divide-and-conquer sequences 
               ...</a>
%H A048724 R. Stephan, <a href="a079944.ps">Table of generating functions</a>
%F A048724 a(n) = Xmult(n, 3) (or n XOR (n<<1)). a(n) = A065621(-n).
%F A048724 a(2n) = 2a(n), a(2n+1) = 2a(n) + 2(-1)^n + 1.
%F A048724 G.f. 1/(1-x) * sum(k>=0, 2^k*(3t-t^3)/(1+t)/(1+t^2), t=x^2^k). - Ralf 
               Stephan (ralf(AT)ark.in-berlin.de), Sep 08 2003
%F A048724 a(n)=sum(k=0, n, (1-(-1)^round(+n/2^k))/2*2^k). - Benoit Cloitre, Apr 
               27 2005
%F A048724 a(n) = A001969(A003188(n)). - Philippe DELEHAM, Apr 29 2005
%F A048724 a(n) = A106409(2*n) for n>0. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               May 02 2005
%F A048724 a(n) = A142149(2*n). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Jul 15 2008
%e A048724 12 = 1100 in binary, 24=11000 and their sum is 10100=20, so a(12)=20.
%e A048724 a(4) = 12 = + 8 + 4 -> - 8 + 4 = -4.
%t A048724 Table[ BitXor[2n, n], {n, 0, 65}] (from Robert G. Wilson v (rgwv(at)rgwv.com), 
               Jul 06 2006)
%Y A048724 Cf. A048720, A048725, A048726, A048728. Bisection of A003188.
%Y A048724 See also A065620, A065621.
%Y A048724 Sequence in context: A007479 A076535 A095359 this_sequence A115389 A121867 
               A009193
%Y A048724 Adjacent sequences: A048721 A048722 A048723 this_sequence A048725 A048726 
               A048727
%K A048724 nonn,nice,easy
%O A048724 0,2
%A A048724 Antti Karttunen, Apr 26, 1999

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