A198971 a(n) = 5*10^n - 1.

4, 49, 499, 4999, 49999, 499999, 4999999, 49999999, 499999999, 4999999999, 49999999999, 499999999999, 4999999999999, 49999999999999, 499999999999999, 4999999999999999, 49999999999999999, 499999999999999999, 4999999999999999999, 49999999999999999999, 499999999999999999999

Offset: 0

Author

Vincenzo Librandi, Nov 02 2011

Keywords

• nonn
• easy

Comments

Also maximal value of GCD of 2 distinct (n+1)-digit numbers (compare with A126687). - Michel Marcus, Jun 24 2013

Also, a(n) is the largest obtained remainder when an (n+1)-digit number m is divided by any k with 1 <= k <= m. This remainder is obtained when 10^(n+1)-1 is divided by 5*10^n, example: 999 = 500 * 1 + 499, and a(2) = 499. - Bernard Schott, Nov 23 2021

Also numbers k whose digital reversal equals 2*(k - 2). - Stefano Spezia, Sep 15 2024

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (11,-10).

Crossrefs

Cf. A002283, A086940, A086942, A099150, A126687.

Programs

Magma

[5*10^n-1 : n in [0..20]];

Mathematica

CoefficientList[Series[(4 + 5*x)/(1 - 11*x + 10*x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Jan 03 2013 *)
LinearRecurrence[{11,-10},{4,49},20] (* Harvey P. Dale, Dec 30 2018 *)

PARI

a(n)=5*10^n-1 \\ Charles R Greathouse IV, Oct 07 2015

Formula

a(n) = 10*a(n-1) + 9.

a(n) = 11*a(n-1) - 10*a(n-2), n>1.

G.f.: (4 + 5*x)/(1 - 11*x + 10*x^2). - Vincenzo Librandi, Jan 03 2013

E.g.f.: exp(x)*(5*exp(9*x) - 1). - Stefano Spezia, Nov 17 2022

a(n) = A086942(n+1)/8 = A086940(n+1)/4 = A099150(n+1)/2. - Elmo R. Oliveira, May 02 2025