A239525 For 0 <= n <= 100, a(n) is smallest integer N such that some x/N rounds to n%, with x > 0.

200, 67, 40, 29, 23, 19, 16, 14, 12, 11, 10, 9, 8, 8, 7, 13, 19, 6, 11, 16, 5, 14, 9, 13, 17, 4, 19, 11, 18, 7, 10, 13, 19, 3, 29, 17, 11, 8, 8, 18, 5, 17, 12, 7, 9, 11, 13, 15, 21, 35, 2, 35, 21, 15, 13, 11, 9, 7, 12, 17, 5, 18, 8, 8, 11, 17, 29, 3, 19, 13, 10, 7, 18, 11, 19, 4, 17, 13, 9, 14, 5, 16, 11, 6, 19, 13, 7, 8, 8, 9, 10, 11, 12, 14, 16, 19, 23, 29, 40, 67, 1

Offset

0,1

Comments

When the fractional part is 0.5, rounding in either direction is allowed.

Links

Table of n, a(n) for n=0..100.

Formula

Find the smallest N such that there is some x > 0 with abs(100*x/N - n) <= 0.5.

Example

a(31)=13 because 4/13 = 0.31 (to two digits after the decimal point).

Mathematica

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

Crossrefs

Cf. A239526 (corresponding x).

Sequence in context: A189580 A094220 A035881 * A180104 A114984 A192545

Adjacent sequences: A239522 A239523 A239524 * A239526 A239527 A239528

Keyword

nonn,base,easy,fini,full

Author

Patrick D McLean, Mar 21 2014

Extensions

Edited by Jonathan Dushoff, Apr 22 2022

Status

approved