Search: id:A070939
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%I A070939
%S A070939 1,1,2,2,3,3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,
%T A070939 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,
%U A070939 7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7
%N A070939 Length of binary representation of n.
%C A070939 Zero is assumed to be represented as 0.
%C A070939 For n>1, n appears 2^(n-1) times. - Lekraj Beedassy (blekraj(AT)yahoo.com), 
               Apr 12 2006
%C A070939 a(n) is the permanent of the n X n 0-1 matrix whose (i,j) entry is 1 
               iff i=1 or i=j or i=2*j. For example, a(4)=3 is per([[1, 1, 1, 1], 
               [1, 1, 0, 0], [0, 0, 1, 0], [0, 1, 0, 1]]). - David Callan (callan(AT)stat.wisc.edu), 
               Jun 07 2006
%D A070939 G. Everest, A. van der Poorten, I. Shparlinski and T. Ward, Recurrence 
               Sequences, Amer. Math. Soc., 2003; see esp. p. 255.
%H A070939 T. D. Noe, <a href="b070939.txt">Table of n, a(n) for n = 0..1024</a>
%H A070939 R. Stephan, <a href="somedcgf.html">Some divide-and-conquer sequences 
               ...</a>
%H A070939 R. Stephan, <a href="a079944.ps">Table of generating functions</a>
%H A070939 R. Stephan, <a href="http://arXiv.org/abs/math.CO/0307027">Divide-and-conquer 
               generating functions. I. Elementary sequences</a>
%H A070939 <a href="Sindx_Cor.html#core">Index entries for "core" sequences</a>
%H A070939 <a href="Sindx_Bi.html#binary">Index entries for sequences related to 
               binary expansion of n</a>
%F A070939 a(0) = 1; for n >= 1, a(n) = 1 + floor(log_2(n)) = 1 + A000523(n).
%F A070939 G.f.: 1 + 1/(1-x) * Sum(k>=0, x^2^k). - Ralf Stephan (ralf(AT)ark.in-berlin.de), 
               Apr 12 2002
%F A070939 a(0)=1, a(1)=1 and a(n)=1+a(floor(n/2)) - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Dec 02 2003
%F A070939 a(n) = A000120(n) + A023416(n). - Lekraj Beedassy (blekraj(AT)yahoo.com), 
               Apr 12 2006
%e A070939 8 = 1000 in binary has length 4.
%p A070939 A070939 := proc(n); Digits := 20: if n=0 then 1 else 1+floor(evalf(0.0000001 
               + log(n)/log(2))); fi; end;
%t A070939 Table[Length[IntegerDigits[n, 2]], {n, 0, 50}] - Stefan Steinerberger 
               (stefan.steinerberger(AT)gmail.com), Apr 01 2006
%o A070939 (PARI) a(n)=if(n<1,n==0,floor(log(n)/log(2))+1)
%Y A070939 Cf. A070940, A070941, A001511, A000523.
%Y A070939 A029837(n+1) gives the length of binary representation of n without the 
               leading zeros (i.e. when zero is represented as the empty sequence). 
               For n>0 this is equal to a(n).
%Y A070939 This is Guy Steele's sequence GS(4, 4) (see A135416).
%Y A070939 Sequence in context: A072660 A075172 A029837 this_sequence A113473 A122027 
               A112751
%Y A070939 Adjacent sequences: A070936 A070937 A070938 this_sequence A070940 A070941 
               A070942
%K A070939 nonn,easy,nice,core
%O A070939 0,3
%A A070939 N. J. A. Sloane (njas(AT)research.att.com), May 18 2002
%E A070939 a(4) corrected by Antti Karttunen, Feb 28 2003

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