A110592 Number of digits in base-5 representation of n. String length of A007091.

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, 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, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3

Offset: 0

Author

Jonathan Vos Post, Jul 29 2005

Keywords

• nonn
• base
• easy

Comments

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.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000

Crossrefs

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

Programs

Mathematica

Join[{1},IntegerLength[Range[110],5]] (* Harvey P. Dale, Aug 03 2016 *)

Formula

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

a(n) = floor(log_5(n)) + 1 for n >= 1. - Petros Hadjicostas, Dec 12 2019