A002279 a(n) = 5*(10^n - 1)/9.

0, 5, 55, 555, 5555, 55555, 555555, 5555555, 55555555, 555555555, 5555555555, 55555555555, 555555555555, 5555555555555, 55555555555555, 555555555555555, 5555555555555555, 55555555555555555, 555555555555555555, 5555555555555555555, 55555555555555555555, 555555555555555555555

Offset: 0

Author

N. J. A. Sloane

Keywords

• easy
• nonn

Comments

Arithmetic mean of all n-digit odd numbers. E.g., a(2) = arithmetic mean of {11,13,15,...,97,99} = (11+99)/2 = 55. - Amarnath Murthy, Aug 02 2005

Links

• Ivan Panchenko, Table of n, a(n) for n = 0..200
• Eric Weisstein's World of Mathematics, Repdigit.
• Index entries for linear recurrences with constant coefficients, signature (11,-10).

Crossrefs

Cf. A002283, A178632, A010785.

Cf. A002275, A002276, A002277, A002278, A002280, A002281, A002282, A075415.

Programs

Mathematica

Table[FromDigits[PadRight[{},n,5]],{n,0,20}] (* Harvey P. Dale, Oct 05 2013 *)

Maxima

A002279(n):=5*(10^n-1)/9$
makelist(A002279(n),n,0,30); /* Martin Ettl, Nov 08 2012 */

PARI

a(n)=5*(10^n-1)/9 \\ Charles R Greathouse IV, Sep 24 2015

Python

def A002279(n): return 5*(10**n-1)//9 # Karl-Heinz Hofmann, Nov 28 2023

Formula

a(n) = A178632(n)/A002283(n). - Reinhard Zumkeller, May 31 2010

From Vincenzo Librandi, Jul 22 2010: (Start)

a(n) = a(n-1) + 5*10^(n-1) with a(0)=0.

a(n) = 11*a(n-1) - 10*a(n-2) with a(0)=0, a(1)=5. (End)

G.f.: 5*x/((1 - x)*(1 - 10*x)). - Ilya Gutkovskiy, Feb 24 2017

E.g.f.: 5*exp(x)*(exp(9*x) - 1)/9. - Stefano Spezia, Sep 13 2023

From Karl-Heinz Hofmann, Nov 28 2023: (Start)

a(n) = A010785(9*n-4) for n > 0.

a(n) = 5 * A002275(n).

a(n) = 5 * A002283(n) / 9. (End)