A133296 Smallest number whose sum of digits is 2n.

0, 2, 4, 6, 8, 19, 39, 59, 79, 99, 299, 499, 699, 899, 1999, 3999, 5999, 7999, 9999, 29999, 49999, 69999, 89999, 199999, 399999, 599999, 799999, 999999, 2999999, 4999999, 6999999, 8999999, 19999999, 39999999, 59999999, 79999999, 99999999, 299999999, 499999999

Offset: 0

Author

Paul Curtz, Oct 17 2007

Keywords

• nonn
• base
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,100,-100).

Crossrefs

Bisection of A051885 (even part).

Cf. A131668.

Programs

Maple

a:= n-> parse(cat(irem(2*n, 9, 'r'), 9$r)):
seq(a(n), n=0..38);  # Alois P. Heinz, Mar 12 2025

Mathematica

a[n_] := (Mod[2n, 9] + 1)*10^Floor[2n/9] - 1; Table[a[n], {n, 0,38}] (* James C. McMahon, Mar 13 2025 *)

Formula

From Alois P. Heinz, Mar 12 2025: (Start)

G.f.: x*(20*x^8+20*x^7+20*x^6+20*x^5+11*x^4+2*x^3+2*x^2+2*x+2)/((x-1)*(100*x^9-1)).

a(n) = A051885(2*n). (End)