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A110591 Number of digits in base-4 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 (list; graph; refs; listen; history; text; internal format)
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
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
MAPLE
A110592 := proc(n)
if n = 0 then
1;
else
1+floor(log[4](n)) ;
end if;
end proc:
seq(A110592(n), n=0..50) ; # R. J. Mathar, Sep 02 2020
MATHEMATICA
a[n_] := If[n == 0, 1, Floor[Log[4, n]] + 1];
a /@ Range[0, 100] (* Jean-François Alcover, Nov 24 2020 *)
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
Sequence in context: A211667 A001069 A156877 * A105209 A179076 A095861
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Jul 29 2005
STATUS
approved

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Last modified February 24 14:16 EST 2024. Contains 370304 sequences. (Running on oeis4.)