A113473 n repeated 2^(n-1) times.
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, 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, 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
Offset: 1
Examples
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
Programs
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Mathematica
a[ n_] := If[ n < 1, 0, BitLength[n]]; (* Michael Somos, Jun 02 2019 *) Table[PadRight[{},2^(n-1),n],{n,10}]//Flatten (* Harvey P. Dale, Dec 07 2024 *)
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PARI
for(n=1,9,for(i=1,1<<(n-1),print1(n", "))) \\ Charles R Greathouse IV, Jun 11 2011
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PARI
{a(n) = if( n<1, 0, exponent(n)+1)}; /* Michael Somos, Jun 02 2019 */ -
Python
def A113473(n): return n.bit_length() # Chai Wah Wu, Oct 14 2022
Formula
a(1) = 1; for n>1 a(n) = a(floor(n/2)) + 1.
a(n) = floor(log_2(2n)).
It appears that a(n) = Sum_{k=0..n-1} (1-(-1)^A000108(k))/2. - Paul Barry, Mar 31 2008
a(n) = A070939(n) if n>0. - R. J. Mathar, Aug 13 2008
a(n) = A029837(n+1) = 1 + floor(log_2(n)) if n>0. - Michael Somos, Jun 02 2019