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

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

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

Cf. A002283, A126687.

Sequence in context: A355481 A362479 A173038 * A348547 A348425 A273230

Adjacent sequences: A198968 A198969 A198970 * A198972 A198973 A198974

Keyword

nonn,easy

Author

Vincenzo Librandi, Nov 02 2011

Status

approved