A110592 - OEIS

%I #23 Dec 13 2019 05:35:02

%S 1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,

%T 3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,

%U 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

%N Number of digits in base-5 representation of n. String length of A007091.

%C In terms of the repetition convolution operator #, where (sequence A) # (sequence B) = the sequence consisting of A(n) copies of B(n), then this sequence is the repetition convolution A110595 # 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 G. C. Greubel, <a href="/A110592/b110592.txt">Table of n, a(n) for n = 0..5000</a>

%F G.f.: 1 + (1/(1 - x))*Sum_{k>=0} x^(5^k). - _Ilya Gutkovskiy_, Jan 08 2017

%F a(n) = floor(log_5(n)) + 1 for n >= 1. - _Petros Hadjicostas_, Dec 12 2019

%t Join[{1},IntegerLength[Range[110],5]] (* _Harvey P. Dale_, Aug 03 2016 *)

%Y Cf. A007091, A081604, A110590, A110595, A330358.

%K nonn,base,easy

%O 0,6

%A _Jonathan Vos Post_, Jul 29 2005