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
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]