

A110591


Number of digits in base4 representation of n.


11



1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4
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OFFSET

0,5


COMMENTS

Number of digits in A007090(n).
In terms of the repetition convolution operator #, where (sequence A) # (sequence B) = the sequence consisting of A(n) copies of B(n), this sequence is the repetition convolution A110594 # n. Over the set of positive infinite integer sequences, # gives a nonassociative noncommutative groupoid (magma) with a left identity (A000012) but no right identity, where the left identity is also a right nullifier and idempotent. For any positive integer constant c, the sequence c*A000012 = (c,c,c,c,...) is also a right nullifier; for c = 1, this is A000012; for c = 3 this is A010701.


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000


FORMULA

G.f.: 1 + (1/(1  x))*Sum_{k>=0} x^(4^k).  Ilya Gutkovskiy, Jan 08 2017
a(n) = floor(log_4(n)) + 1 for n >= 1.  Petros Hadjicostas, Dec 12 2019


PROG

(Haskell)
import Data.List (unfoldr)
a110591 0 = 1
a110591 n = length $
unfoldr (\x > if x == 0 then Nothing else Just (x, x `div` 4)) n
 Reinhard Zumkeller, Apr 22 2011


CROSSREFS

Cf. A000012, A007090, A010701, A049804, A081604, A110594.
Sequence in context: A211667 A001069 A156877 * A105209 A179076 A095861
Adjacent sequences: A110588 A110589 A110590 * A110592 A110593 A110594


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, Jul 29 2005


STATUS

approved



