A083445 Largest n-digit number minus the product of its digits; i.e., a(n) = 99999... (n 9's) - 9^n.

18, 270, 3438, 40950, 468558, 5217030, 56953278, 612579510, 6513215598, 68618940390, 717570463518, 7458134171670, 77123207545038, 794108867905350, 8146979811148158, 83322818300333430, 849905364703000878, 8649148282327007910, 87842334540943071198

Offset

2,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 2..1000

Index entries for linear recurrences with constant coefficients, signature (20, -109, 90).

Formula

a(n) = (10^n - 1) - 9^n.

a(n) = 20*a(n-1) - 109*a(n-2) + 90*a(n-3) with a(2)=18, a(3)=270, a(4)=3438. - Harvey P. Dale, Sep 05 2015

G.f.: 18*x^2*(1 - 5*x) / ((1 - x)*(1 - 9*x)*(1 - 10*x)). - Colin Barker, Jul 29 2017

Mathematica

Table[10^n-9^n-1, {n, 2, 20}] (* or *) LinearRecurrence[{20, -109, 90}, {18, 270, 3438}, 20] (* Harvey P. Dale, Sep 05 2015 *)

Prog

(Magma) [(10^n-1)-9^n: n in [2..20]]; // Vincenzo Librandi, Jul 29 2017
(PARI) Vec(18*x^2*(1 - 5*x) / ((1 - x)*(1 - 9*x)*(1 - 10*x)) + O(x^30)) \\ Colin Barker, Jul 29 2017

Crossrefs

Cf. A083446.

Sequence in context: A080583 A273589 A076693 * A159740 A115903 A004357

Adjacent sequences: A083442 A083443 A083444 * A083446 A083447 A083448

Keyword

base,easy,nonn

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 01 2003

Extensions

More terms from Michel ten Voorde Jun 13 2003

Status

approved