A178500 a(n) = 10^n * signum(n).

0, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000, 10000000000, 100000000000, 1000000000000, 10000000000000, 100000000000000, 1000000000000000, 10000000000000000, 100000000000000000, 1000000000000000000, 10000000000000000000, 100000000000000000000

Offset: 0

Author

Reinhard Zumkeller, May 28 2010

Keywords

• nonn
• easy

Comments

a(n-1) is the minimum 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 (10).

Crossrefs

Cf. A000533, A011557, A057427, A061601, A070565, A109002, A155559, A178501.

Partial sums of A063945.

Programs

Mathematica

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

Formula

a(n) = A011557(n)*A057427(n).

For n > 0, a(n) = A011557(n).

a(n) = 10*A178501(n).

a(n) = A000533(n) - 1.

A061601(a(n)) = A109002(n+1).

From Elmo R. Oliveira, Jul 21 2025: (Start)

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

E.g.f.: 2*exp(5*x)*sinh(5*x).

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