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

1,2

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).

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)

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 *)

Crossrefs

Cf. A051885, A069532.

Sequence in context: A067063 A075023 A363099 * A302556 A088262 A110406

Adjacent sequences: A205957 A205958 A205959 * A205961 A205962 A205963

Keyword

base,easy,nonn

Author

Arkadiusz Wesolowski, Feb 02 2012

Status

approved