Search: id:A000523
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%I A000523
%S A000523 0,1,1,2,2,2,2,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,
%T A000523 5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,
%U A000523 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6
%N A000523 Log_2(n) rounded down.
%C A000523 Or, n-1 appears 2^(n-1) times. - Jon Perry (perry(AT)globalnet.co.uk), 
               Sep 21 2002
%C A000523 a(n) + 1 = number of bits in binary expansion of n.
%C A000523 Largest power of 2 dividing LCM[1..n]: A007814[A003418(n)].
%C A000523 Log_2(0) = -infinity.
%C A000523 Also max(Omega(k): 1<=k<=n), where Omega(n)=A001222(n), number of prime 
               factors with repetition; see A080613. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Feb 25 2003
%C A000523 a(n+1) = number of digits of n-th number with no 0 in ternary representation 
               = A081604(A032924(n)); A107680(n) = A003462(a(n+1)). - Reinhard Zumkeller 
               (reinhard.zumkeller(AT)gmail.com), May 20 2005
%C A000523 a(n) = A152487(n-1,0) = A152487(n,1). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Dec 06 2008]
%D A000523 G. H. Hardy, Note on Dr. Vacca's series..., Quart. J. Pure Appl. Math. 
               43 (1912) 215-216.
%D A000523 D. E. Knuth, The Art of Computer Programming, Vol. 1: Fundamental Algorithms, 
               p. 400.
%H A000523 N. J. A. Sloane, <a href="b000523.txt">Table of n, a(n) for n = 1..10000</
               a>
%H A000523 R. Stephan, <a href="somedcgf.html">Some divide-and-conquer sequences 
               ...</a>
%H A000523 R. Stephan, <a href="a079944.ps">Table of generating functions</a>
%F A000523 a(n) = if n > 1 then a(floor(n / 2)) + 1 else 0. - Reinhard Zumkeller 
               (reinhard.zumkeller(AT)gmail.com), Oct 29 2001
%F A000523 G.f.: 1/(1-x) * Sum(k>=1, x^2^k). - Ralf Stephan (ralf(AT)ark.in-berlin.de), 
               Apr 13 2002
%e A000523 a(5)=2 because the binary expansion of 5 (=101) has three bits.
%p A000523 A000523 := n->floor(simplify(log(n)/log(2)));
%p A000523 A000523 := proc(n) local nn,i; if(0 = n) then RETURN(-infinity); fi; 
               nn := n; for i from -1 to n do if(0 = nn) then RETURN(i); fi; nn 
               := floor(nn/2); od; end;
%o A000523 (MAGMA) [Ilog2(n) : n in [1..130] ];
%o A000523 (PARI) a(n)=if(n<1,0,floor(log(n)/log(2)))
%Y A000523 Cf. A029837. Partial sums: A061168.
%Y A000523 Cf. A000195, A000193, A004233.
%Y A000523 a(n) = A070939(n)-1 for n>=1.
%Y A000523 Sequence in context: A072750 A029835 A074280 this_sequence A124156 A072749 
               A066490
%Y A000523 Adjacent sequences: A000520 A000521 A000522 this_sequence A000524 A000525 
               A000526
%K A000523 nonn,easy,nice
%O A000523 1,4
%A A000523 N. J. A. Sloane (njas(AT)research.att.com).
%E A000523 Error in 4th term, pointed out by Joe Keane (jgk(AT)jgk.org), has been 
               corrected.
%E A000523 More terms from Michael Somos, Aug 02, 2002

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