OFFSET
0,1
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).
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
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 *)
PROG
(Magma) [5*10^n-1 : n in [0..20]];
(PARI) a(n)=5*10^n-1 \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Nov 02 2011
STATUS
approved