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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.

%I A239526 #17 Jun 28 2025 21:27:26
%S A239526 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,
%T A239526 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,
%U A239526 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
%N 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.
%e A239526 a(31)=4 because 4/13=0.31 (2DP).
%t A239526 Table[LinearProgramming[{1, 0}, {{-n/100 + 0.005, 1}, {n/100 + 0.005, -1}}, {0, 0}, {1, 1}, Integers], {n, 0, 100}] // Transpose // Last
%o A239526 (Python)
%o A239526 from itertools import count
%o A239526 def A239526(n):
%o A239526     for y in count(1):
%o A239526         x, z = divmod(y*((n<<1)+1),200)
%o A239526         if not z: return x
%o A239526         x, z = divmod(y*((n<<1)-1),200)
%o A239526         if (x:=x+bool(z)) and (200*x+y)//(y<<1) == n:
%o A239526             return x # _Chai Wah Wu_, Jun 28 2025
%Y A239526 Cf. A239525 (Minimal sample sizes).
%K A239526 fini,nonn,base
%O A239526 0,16
%A A239526 _Patrick D McLean_, Mar 21 2014