login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A247890 Number of digits in (R_n)^n. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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(log((10 - 10^(1-n))/9)) / log(10)) + n * (n - 1) + 1. (End)

LINKS

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

FORMULA

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.

Conjectures from Colin Barker, Oct 28 2017: (Start)

G.f.: x*(1 + x + 2*x^2 + 2*x^3 + 2*x^4 + 2*x^5 + 2*x^6 + 2*x^7 + 2*x^8 + 2*x^9 + 2*x^10 + 2*x^11 + 2*x^12 + 2*x^13 + 2*x^14 + 2*x^15 + 2*x^16 + 2*x^17 + 2*x^18 + 2*x^19 + 2*x^20 + 3*x^21 + x^23) / ((1 - x)^3*(1 + x)*(1 - x + x^2 - x^3 + x^4 - x^5 + x^6 - x^7 + x^8 - x^9 + x^10)*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 + x^10)).

a(n) = 2*a(n-1) - a(n-2) + a(n-22) - 2*a(n-23) + a(n-24) for n>24.

(End)

MATHEMATICA

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 *)

PROG

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

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

CROSSREFS

Cf. A002061, A014206, A002275.

Sequence in context: A025728 A084537 A002061 * A063541 A206246 A171965

Adjacent sequences:  A247887 A247888 A247889 * A247891 A247892 A247893

KEYWORD

nonn,easy,base

AUTHOR

Derek Orr, Sep 25 2014

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified February 24 03:21 EST 2018. Contains 299595 sequences. (Running on oeis4.)