A109002 Maximal difference between two n-digit numbers.

9, 89, 899, 8999, 89999, 899999, 8999999, 89999999, 899999999, 8999999999, 89999999999, 899999999999, 8999999999999, 89999999999999, 899999999999999

Offset

1,1

Comments

a(n) = A061601(A178500(n-1)). - Reinhard Zumkeller, May 28 2010

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.

a(n+1) = 10*a(n) + 9. - Reinhard Zumkeller, May 28 2010

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

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], [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

Sequence in context: A072256 A138288 A059482 * A142991 A152267 A082147

Adjacent sequences: A108999 A109000 A109001 * A109003 A109004 A109005

Keyword

base,easy,nonn

Author

Amarnath Murthy, Aug 14 2005

Status

approved