A205960 Smallest odd number with digit sum equal to n.

1, 11, 3, 13, 5, 15, 7, 17, 9, 19, 29, 39, 49, 59, 69, 79, 89, 99, 199, 299, 399, 499, 599, 699, 799, 899, 999, 1999, 2999, 3999, 4999, 5999, 6999, 7999, 8999, 9999, 19999, 29999, 39999, 49999, 59999, 69999, 79999, 89999, 99999, 199999, 299999, 399999, 499999

Offset: 1

Author

Arkadiusz Wesolowski, Feb 02 2012

Keywords

• base
• easy
• nonn

Comments

Except for a(2), a(4), a(6) and a(8), the same as A051885 (n>0).

Links

• Arkadiusz Wesolowski, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,10,-10).

Crossrefs

Cf. A051885, A069532.

Programs

Mathematica

e = 5; Join[Table[l = 1; While[True, a = 2*l - 1; If[Total[IntegerDigits[a]] == n, Break[]]; l++]; a, {n, 8}], Flatten[Table[i*10^j - 1, {j, e}, {i, 9}]]]
With[{ds=Table[{n,Total[IntegerDigits[n]]},{n,1,600001,2}]},Table[ SelectFirst[ ds,#[[2]]==k&],{k,50}]][[All,1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 30 2018 *)

Formula

a(n+1) = A069532(n) + 1.

From Chai Wah Wu, Sep 15 2020: (Start)

a(n) = a(n-1) + 10*a(n-9) - 10*a(n-10) for n > 18.

G.f.: x*(90*x^17 - 90*x^16 + 90*x^15 - 90*x^14 + 90*x^13 - 90*x^12 + 90*x^11 - 90*x^10 - 8*x^8 + 10*x^7 - 8*x^6 + 10*x^5 - 8*x^4 + 10*x^3 - 8*x^2 + 10*x + 1)/((x - 1)*(10*x^9 - 1)). (End)