A066007 a(n) is that n-digit number m which minimizes m/(sum of digits of m); in case of a tie pick the smallest.

1, 19, 199, 1099, 10999, 109999, 1099999, 10999999, 109999999, 1099999999, 10999999999, 109999999999, 1099999999999, 10999999999999, 100999999999999, 1009999999999999, 10099999999999999, 100999999999999999, 1009999999999999999, 10099999999999999999

Offset: 1

Author

N. J. A. Sloane, Dec 11 2001

Keywords

• nonn
• base
• easy

Links

• S. W. Golomb, Sums and products of digits, IEEE Information Theory Society Newsletter, 51 (No. 3, Sept. 2001), p. 15.
• S. W. Golomb, Sums and Products of Digits Solutions, IEEE Information Theory Society Newsletter, Vol. 67, No. 1, March 2017, p. 22. Reprint.

Crossrefs

Cf. A066008, A034726, A034727.

Programs

Python

def k(r): return (10**r - 1)//9 + r + 2
def a(n):
  r = 0
  while k(r+1) <= n: r += 1
  return int('1' + '0'*r + '9'*(n-r-1))
print([a(n) for n in range(1, 21)]) # Michael S. Branicky, Jan 19 2021

Formula

1 followed by 0's followed by 9's; the first time r 0's appear is at n = (10^r-1)/9+r+2.