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1, 2, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 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, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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COMMENTS
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Sequence consists of A011782(n) n+1's. - Jon Perry, Apr 04 2004
For n > 0: a(n) = A003314(n+1) - A003314(n) = A123753(n) - A123753(n-1). - Reinhard Zumkeller, Oct 12 2006
For k >= 2, k appears 2^(k-2) times consecutively. - Bernard Schott, Jun 08 2019
Also length of binary representation of 2n. - Michel Marcus, Oct 28 2020
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LINKS
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Table of n, a(n) for n=0..92.
Index entries for sequences related to binary expansion of n
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FORMULA
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Let b(1)=1, b(n) = a(n-floor(n/2)) + 1, then a(n) = b(n+1). - Benoit Cloitre, Oct 23 2002
G.f.: 1/(1-x) * (1 + Sum_{k>=0} x^2^k). - Ralf Stephan, Apr 15 2002
a(n) = ceiling(log_2(n+1)) + 1 = A029837(n+1) + 1. - Ralf Stephan, Apr 15 2002
a(n) = ceiling(average of previous entries) + 1. - Jon Perry, Apr 04 2004
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MATHEMATICA
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Table[IntegerLength[n, 2], {n, 1, 201, 2}] (* Harvey P. Dale, May 17 2011 *)
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PROG
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(PARI) a(n)=length(binary(2*n+1))
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CROSSREFS
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Bisection of A070939 and also of A070940.
Sequence in context: A303660 A290021 A348020 * A061775 A225634 A247134
Adjacent sequences: A070938 A070939 A070940 * A070942 A070943 A070944
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, May 18 2002
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STATUS
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approved
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