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A073642
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Replace 2^k in the binary representation of n with k (i.e. if n = 2^a+2^b+2^c+... then a(n)=a+b+c+...).
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9
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0, 0, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 6, 6, 4, 4, 5, 5, 6, 6, 7, 7, 7, 7, 8, 8, 9, 9, 10, 10, 5, 5, 6, 6, 7, 7, 8, 8, 8, 8, 9, 9, 10, 10, 11, 11, 9, 9, 10, 10, 11, 11, 12, 12, 12, 12, 13, 13, 14, 14, 15, 15, 6, 6, 7, 7, 8, 8, 9, 9, 9, 9, 10, 10, 11, 11, 12, 12, 10, 10, 11, 11, 12, 12, 13, 13
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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FORMULA
| It seems that for n>10 a(n) < n/Log(n)/2 and that sum(k=1, n, a(k)) is asymptotic to C*n*Log(n)^2 with 1/2>C>0.47
a(1)=0, a(2n) = a(n)+e1(n), a(2n+1) = a(2n), where e1(n) = A000120(n). - Ralf Stephan, Jun 19 2003
a(n) = if n=2^log2(n) then log2(n) else log2(n)+a(n-2^log2(n)), where log2=A000523. a(2*n+1) = a(2*n), as 2^0 = 1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 17 2003
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EXAMPLE
| 9=2^3+2^0 hence a(9)=3+0=3 25=2^4+2^3+2^0 hence a(25)=4+3+0=7
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MAPLE
| A073642 := proc(n)
local bdgs ;
bdgs := convert(n, base, 2) ;
add( op(i, bdgs)*(i-1), i=1..nops(bdgs)) ;
end proc: # R. J. Mathar, Nov 17 2011
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PROG
| (PARI) a(n)=sum(i=1, length(binary(n)), component(binary(n), i)*(length(binary(n))-i))
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CROSSREFS
| a(n) = log_2(A059867(n)).
Cf. A059867, a(n) = A029931(floor(n/2)).
Cf. A087135, A000009, A087136.
Sequence in context: A033270 A103264 A060960 * A108356 A055656 A078571
Adjacent sequences: A073639 A073640 A073641 * A073643 A073644 A073645
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KEYWORD
| easy,nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 29 2002
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EXTENSIONS
| a(0)=0 and offset corrected by Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Apr 20 2009
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