A061219 a(n) is the largest number which can be formed with no zeros, using least number of digits and having digit sum = n.

1, 2, 3, 4, 5, 6, 7, 8, 9, 91, 92, 93, 94, 95, 96, 97, 98, 99, 991, 992, 993, 994, 995, 996, 997, 998, 999, 9991, 9992, 9993, 9994, 9995, 9996, 9997, 9998, 9999, 99991, 99992, 99993, 99994, 99995, 99996, 99997, 99998, 99999, 999991, 999992, 999993, 999994

Offset: 1

Author

Amarnath Murthy, Apr 22 2001

Keywords

• nonn
• base

Comments

a(n) is the digit reversal of terms of A051885 giving such smallest numbers.

Examples

			a(22) = 994, digit sum = 22.
a(100) = 999999999991.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..9000

Crossrefs

Cf. A051885.

Programs

Mathematica

dsn[n_]:=Module[{d=Quotient[n,9]},FromDigits[PadLeft[{n-9d},d,9]]]; If[Divisible[#,10],#/10,#]&/@Array[dsn,50,10] (* Harvey P. Dale, Dec 08 2013 *)

Python

def a(n): return int("9"*(n//9)+str(n%9)*(n%9>0))
print([a(n) for n in range(1, 50)]) # Michael S. Branicky, Aug 16 2023

Extensions

More terms from Harvey P. Dale, Dec 08 2013

Offset corrected by Michael S. Branicky, Aug 16 2023