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A110591 Number of digits in base-4 representation of n. 11

%I

%S 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,

%T 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,

%U 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

%N Number of digits in base-4 representation of n.

%C Number of digits in A007090(n).

%C 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.

%H Reinhard Zumkeller, <a href="/A110591/b110591.txt">Table of n, a(n) for n = 0..10000</a>

%F G.f.: 1 + (1/(1 - x))*Sum_{k>=0} x^(4^k). - _Ilya Gutkovskiy_, Jan 08 2017

%F a(n) = floor(log_4(n)) + 1 for n >= 1. - _Petros Hadjicostas_, Dec 12 2019

%o (Haskell)

%o import Data.List (unfoldr)

%o a110591 0 = 1

%o a110591 n = length $

%o unfoldr (\x -> if x == 0 then Nothing else Just (x, x `div` 4)) n

%o -- _Reinhard Zumkeller_, Apr 22 2011

%Y Cf. A000012, A007090, A010701, A049804, A081604, A110594.

%K easy,nonn

%O 0,5

%A _Jonathan Vos Post_, Jul 29 2005

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Last modified February 28 22:24 EST 2020. Contains 332335 sequences. (Running on oeis4.)