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

0,2

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

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

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)

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 *)
LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, 100, -100}, {0, 2, 4, 6, 8, 19, 39, 59, 79, 99}, 40] (* Harvey P. Dale, Jan 16 2026 *)

Crossrefs

Bisection of A051885 (even part).

Cf. A131668.

Sequence in context: A152491 A355557 A329738 * A323333 A076402 A053198

Adjacent sequences: A133293 A133294 A133295 * A133297 A133298 A133299

Keyword

nonn,base,easy

Author

Paul Curtz, Oct 17 2007

Status

approved