A245593 -id:A245593 - cp's OEIS frontend

1, 3, 7, 13, 21, 31, 43, 57, 73, 91, 111, 133, 157, 183, 211, 241, 273, 307, 343, 381, 421, 464, 508, 554, 602, 652, 704, 758, 814, 872, 932, 994, 1058, 1124, 1192, 1262, 1334, 1408, 1484, 1562, 1642, 1724, 1808, 1895, 1983, 2073, 2165, 2259, 2355, 2453, 2553, 2655, 2759, 2865

Offset: 1

Derek Orr, Sep 25 2014

R_n is the n-th repunit (i.e., R_n = 11...111 with n 1's).
From David A. Corneth, Jun 27 2016: (Start)
The number of digits of m is floor(log(m)/log(10)) + 1 for m > 0.
R_n = (10^n - 1) / 9 = (10 - 10^(1-n))/9 * 10^(n-1). Its number of digits is floor(n * log((10 - 10^(1-n))/9) / log(10)) + n * (n - 1) + 1. [corrected by Jason Yuen, Nov 11 2024] (End)

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A002061, A014206, A002275.

Cf. A055642, A245593.

[#Intseq(Floor((10^n-1)/9)^n): n in [1..50]]; // Marius A. Burtea, May 20 2019

Table[IntegerLength[((10^n - 1)/9)^n], {n, 54}] (* or *)
Table[IntegerLength[FromDigits[Table[1, {n}]]^n], {n, 54}] (* Michael De Vlieger, Jun 27 2016 *)

PARI
```
vector(100,n,#Str(((10^n-1)/9)^n))
```

a(n) = logint(((10 - 10^(1-n))/9)^n\1,10)+n^2-n+1 \\ David A. Corneth, Jun 27 2016

def a(n): return len(str(int("1"*n)**n))
print([a(n) for n in range(1, 55)]) # Michael S. Branicky, Apr 20 2022

a(n) = n^2 - n + 1 = A002061(n), for 1 <= n <= 21.
a(n) = n^2 - n + 2 = A014206(n-1), for 22 <= n <= 43.
a(n) = A055642(A245593(n)). - Michel Marcus, Apr 20 2022

Incorrect conjectures removed by Georg Fischer, May 19 2019

cp's OEIS Frontend

A247890 Number of digits in (R_n)^n.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

PARI

PARI

Python

Formula

Extensions