A109002 Maximal difference between two n-digit numbers.

9, 89, 899, 8999, 89999, 899999, 8999999, 89999999, 899999999, 8999999999, 89999999999, 899999999999, 8999999999999, 89999999999999, 899999999999999, 8999999999999999, 89999999999999999, 899999999999999999, 8999999999999999999, 89999999999999999999, 899999999999999999999

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Index entries for linear recurrences with constant coefficients, signature (11,-10).

Formula

a(n) = (10^n - 1) - 10^(n-1), n > 1.

From Reinhard Zumkeller, May 28 2010: (Start)

a(n) = A061601(A178500(n-1)).

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

G.f.: 9*x - x^2*(-89+80*x)/((10*x-1)*(x-1)). - R. J. Mathar, Oct 29 2011

From Elmo R. Oliveira, Jun 12 2025: (Start)

E.g.f.: (1 + 10*x - 10*exp(x) - exp(10*x) + 10*exp(10*x))/10.

a(n) = 11*a(n-1) - 10*a(n-2) for n >= 4. (End)

Example

a(1) = 9 - 0 = 9, a(4) = 9999 - 1000 = 8999.

Mathematica

Join[{9}, Table[FromDigits[PadRight[{8}, n, 9]], {n, 2, 20}]] (* or *) LinearRecurrence[{11, -10}, {9, 89, 899}, 20] (* Harvey P. Dale, May 09 2021 *)

Prog

(Magma) [9] cat [9*10^n-1: n in [1..30]]; // Vincenzo Librandi, Oct 29 2011
(PARI) a(n)=if(n>1, (10^n-1)-10^(n-1), 9) \\ Charles R Greathouse IV, Oct 29 2011

Crossrefs

Cf. A061601, A178500.

Sequence in context: A138288 A370179 A059482 * A142991 A152267 A082147

Adjacent sequences: A108999 A109000 A109001 * A109003 A109004 A109005

Keyword

base,easy,nonn

Author

Amarnath Murthy, Aug 14 2005

Status

approved