A239526 For 0<=n<=100, a(n) is the number of positive responses x such that x/N rounds to n%, minimized over sample size N.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 1, 2, 3, 1, 3, 2, 3, 4, 1, 5, 3, 5, 2, 3, 4, 6, 1, 10, 6, 4, 3, 3, 7, 2, 7, 5, 3, 4, 5, 6, 7, 10, 17, 1, 18, 11, 8, 7, 6, 5, 4, 7, 10, 3, 11, 5, 5, 7, 11, 19, 2, 13, 9, 7, 5, 13, 8, 14, 3, 13, 10, 7, 11, 4, 13, 9, 5, 16, 11, 6, 7, 7, 8, 9, 10, 11, 13, 15, 18, 22, 28, 39, 66, 1

Offset: 0

Author

Patrick D McLean, Mar 21 2014

Keywords

• fini
• nonn
• base

Examples

			a(31)=4 because 4/13=0.31 (2DP).
		

Crossrefs

Cf. A239525 (Minimal sample sizes).

Programs

Mathematica

Table[LinearProgramming[{1, 0}, {{-n/100 + 0.005, 1}, {n/100 + 0.005, -1}}, {0, 0}, {1, 1}, Integers], {n, 0, 100}] // Transpose // Last

Python

from itertools import count
def A239526(n):
    for y in count(1):
        x, z = divmod(y*((n<<1)+1),200)
        if not z: return x
        x, z = divmod(y*((n<<1)-1),200)
        if (x:=x+bool(z)) and (200*x+y)//(y<<1) == n:
            return x # Chai Wah Wu, Jun 28 2025