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

1,2

Links

Table of n, a(n) for n=1..20.

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.

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.

Prog

(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

Crossrefs

Cf. A066008, A034726, A034727.

Sequence in context: A058370 A230012 A164890 * A147830 A135162 A185687

Adjacent sequences: A066004 A066005 A066006 * A066008 A066009 A066010

Keyword

nonn,base,easy

Author

N. J. A. Sloane, Dec 11 2001

Status

approved