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%I #30 Oct 14 2022 16:05:51
%S 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 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,
%U 7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7
%N n repeated 2^(n-1) times.
%F a(1) = 1; for n>1 a(n) = a(floor(n/2)) + 1.
%F a(n) = floor(log_2(2n)).
%F It appears that a(n) = Sum_{k=0..n-1} (1-(-1)^A000108(k))/2. - _Paul Barry_, Mar 31 2008
%F a(n) = A070939(n) if n>0. - _R. J. Mathar_, Aug 13 2008
%F a(n) = A029837(n+1) = 1 + floor(log_2(n)) if n>0. - _Michael Somos_, Jun 02 2019
%e G.f. = x + 2*x^2 + 2*x^3 + 3*x^4 + 3*x^5 + 3*x^6 + 3*x^7 + 4*x^8 + ... - _Michael Somos_, Jun 02 2019
%t a[ n_] := If[ n < 1, 0, BitLength[n]]; (* _Michael Somos_, Jun 02 2019 *)
%o (PARI) for(n=1,9,for(i=1,1<<(n-1),print1(n", "))) \\ _Charles R Greathouse IV_, Jun 11 2011
%o (PARI) {a(n) = if( n<1, 0, exponent(n)+1)}; /* _Michael Somos_, Jun 02 2019 */
%o (Python)
%o def A113473(n): return n.bit_length() # _Chai Wah Wu_, Oct 14 2022
%Y Cf. A029837, A070939.
%Y Partial sums of A036987.
%K nonn,easy
%O 1,2
%A _Zak Seidov_, Jan 08 2006
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