A124167 a(n) = 10*(10^n-1).

0, 90, 990, 9990, 99990, 999990, 9999990, 99999990, 999999990, 9999999990, 99999999990, 999999999990, 9999999999990, 99999999999990, 999999999999990, 9999999999999990, 99999999999999990, 999999999999999990

Offset

0,2

Comments

a(n - 1) is the maximum difference between an n-digit number (written in base 10, nonzero leading digit) and the product of its digits. For n>1, it is also a number meeting that bound. See A070565. - Devin Akman, Apr 17 2019

Links

Michael De Vlieger, Table of n, a(n) for n = 0..999

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

Formula

a(n) = 10*A002283(n).

From G. C. Greubel, Jun 30 2019: (Start)

a(n) = 90*A002275(n).

a(n) = 11*a(n-1) - 10*a(n-2).

G.f.: 10*(1/(1-10*x) - 1/(1-x)).

E.g.f.: 10*(exp(10*x) - exp(x)). (End)

Maple

a:=n->sum (10^(n-j+2)-10^(n-j+1), j=0..n): seq(a(n), n=0..20);

Mathematica

Array[10 (10^# - 1) &, 20, 0] (* Michael De Vlieger, Apr 21 2019 *)

Prog

(PARI) vector(20, n, n--; 10*(10^n -1)) \\ G. C. Greubel, Jun 30 2019
(Magma) [10*(10^n -1): n in [0..20]]; // G. C. Greubel, Jun 30 2019
(Sage) [10*(10^n -1) for n in (0..20)] # G. C. Greubel, Jun 30 2019
(GAP) List([0..20], n-> 10*(10^n -1)) # G. C. Greubel, Jun 30 2019

Crossrefs

Partial sums give 10*A099676.

Cf. A002283, A002275, A070565.

Sequence in context: A101243 A173483 A202960 * A223364 A048548 A013427

Adjacent sequences: A124164 A124165 A124166 * A124168 A124169 A124170

Keyword

easy,nonn

Author

Zerinvary Lajos, Dec 02 2006

Status

approved