A133195 Smallest number whose sum of digits is 3n.

0, 3, 6, 9, 39, 69, 99, 399, 699, 999, 3999, 6999, 9999, 39999, 69999, 99999, 399999, 699999, 999999, 3999999, 6999999, 9999999, 39999999, 69999999, 99999999, 399999999, 699999999, 999999999, 3999999999, 6999999999, 9999999999, 39999999999, 69999999999

Offset: 0

Author

Paul Curtz, Oct 09 2007

Keywords

• nonn
• base
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (1,0,10,-10).

Crossrefs

Cf. A133201.

Programs

Mathematica

LinearRecurrence[{1,0,10,-10},{0,3,6,9},40] (* Harvey P. Dale, Oct 01 2018 *)

Python

def a(n): q, r = divmod(3*n, 9); return int(str(r) + "9"*q)
print([a(n) for n in range(31)]) # Michael S. Branicky, Feb 07 2022

Formula

a(n) = 1/3 * A133201(n).

a(n) = a(n-1)+10*a(n-3)-10*a(n-4). G.f.: 3*x*(x^2+x+1) / ((x-1)*(10*x^3-1)). [Colin Barker, Feb 01 2013]