cp's OEIS Frontend

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

%I A002279 #68 Feb 16 2025 08:32:25
%S A002279 0,5,55,555,5555,55555,555555,5555555,55555555,555555555,5555555555,
%T A002279 55555555555,555555555555,5555555555555,55555555555555,
%U A002279 555555555555555,5555555555555555,55555555555555555,555555555555555555,5555555555555555555,55555555555555555555,555555555555555555555
%N A002279 a(n) = 5*(10^n - 1)/9.
%C A002279 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
%H A002279 Ivan Panchenko, <a href="/A002279/b002279.txt">Table of n, a(n) for n = 0..200</a>
%H A002279 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Repdigit.html">Repdigit</a>.
%H A002279 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-10).
%F A002279 a(n) = A178632(n)/A002283(n). - _Reinhard Zumkeller_, May 31 2010
%F A002279 From _Vincenzo Librandi_, Jul 22 2010: (Start)
%F A002279 a(n) = a(n-1) + 5*10^(n-1) with a(0)=0.
%F A002279 a(n) = 11*a(n-1) - 10*a(n-2) with a(0)=0, a(1)=5. (End)
%F A002279 G.f.: 5*x/((1 - x)*(1 - 10*x)). - _Ilya Gutkovskiy_, Feb 24 2017
%F A002279 E.g.f.: 5*exp(x)*(exp(9*x) - 1)/9. - _Stefano Spezia_, Sep 13 2023
%F A002279 From _Karl-Heinz Hofmann_, Nov 28 2023: (Start)
%F A002279 a(n) = A010785(9*n-4) for n > 0.
%F A002279 a(n) = 5 * A002275(n).
%F A002279 a(n) = 5 * A002283(n) / 9. (End)
%t A002279 Table[FromDigits[PadRight[{},n,5]],{n,0,20}] (* _Harvey P. Dale_, Oct 05 2013 *)
%o A002279 (Maxima) A002279(n):=5*(10^n-1)/9$
%o A002279 makelist(A002279(n),n,0,30); /* _Martin Ettl_, Nov 08 2012 */
%o A002279 (PARI) a(n)=5*(10^n-1)/9 \\ _Charles R Greathouse IV_, Sep 24 2015
%o A002279 (Python)
%o A002279 def A002279(n): return 5*(10**n-1)//9 # _Karl-Heinz Hofmann_, Nov 28 2023
%Y A002279 Cf. A002283, A178632, A010785.
%Y A002279 Cf. A002275, A002276, A002277, A002278, A002280, A002281, A002282, A075415.
%K A002279 easy,nonn
%O A002279 0,2
%A A002279 _N. J. A. Sloane_