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%I #16 Feb 18 2024 01:35:11
%S 1,2,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,
%T 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,
%U 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
%N a(n) = floor(log_2(3n)).
%C Length of the symmetric signed digit expansion of n with q=2 (i.e., the length of the representation of n in the (-1,0,1)_2 number system).
%C n occurs A001045(n) times. - _Amiram Eldar_, Feb 18 2024
%H C. Heuberger and H. Prodinger, <a href="http://dx.doi.org/10.1007/s006070170021">On minimal expansions in redundant number systems: Algorithms and quantitative analysis</a>, Computing 66(2001), 377-393.
%F a(n) = A000523(A008585(n)). - _Reinhard Zumkeller_, Mar 16 2013
%F Sum_{n>=1} (-1)^(n+1)/a(n) = log(2) (A002162). - _Amiram Eldar_, Feb 18 2024
%t Floor[Log[2,3*Range[100]]] (* _Harvey P. Dale_, Oct 15 2016 *)
%o (Haskell)
%o a085423 = a000523 . a008585 -- _Reinhard Zumkeller_, Mar 16 2013
%Y Cf. A005578, A001045.
%Y Cf. A000523, A008585, A002162.
%K nonn,easy
%O 1,2
%A _Ralf Stephan_, Jun 30 2003
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