A085423 a(n) = floor(log_2(3n)).

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, 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, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8

Offset

1,2

Comments

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).

n occurs A001045(n) times. - Amiram Eldar, Feb 18 2024

Links

Table of n, a(n) for n=1..96.

C. Heuberger and H. Prodinger, On minimal expansions in redundant number systems: Algorithms and quantitative analysis, Computing 66(2001), 377-393.

Formula

a(n) = A000523(A008585(n)). - Reinhard Zumkeller, Mar 16 2013

Sum_{n>=1} (-1)^(n+1)/a(n) = log(2) (A002162). - Amiram Eldar, Feb 18 2024

Mathematica

Floor[Log[2, 3*Range[100]]] (* Harvey P. Dale, Oct 15 2016 *)

Prog

(Haskell)
a085423 = a000523 . a008585  -- Reinhard Zumkeller, Mar 16 2013

Crossrefs

Cf. A005578, A001045.

Cf. A000523, A008585, A002162.

Sequence in context: A262070 A117806 A351115 * A260998 A361110 A324728

Adjacent sequences: A085420 A085421 A085422 * A085424 A085425 A085426

Keyword

nonn,easy

Author

Ralf Stephan, Jun 30 2003

Status

approved