A232111 Numerator of smallest nonnegative fraction of form +- 1 +- 1/2 +- 1/3 ... +- 1/n.

0, 1, 1, 1, 1, 7, 1, 11, 13, 11, 11, 23, 23, 607, 251, 251, 25, 97, 97, 3767, 3767, 3767, 457, 24319, 24319, 7951, 4261, 13703, 13703, 872843, 872843, 17424097, 13828799, 902339, 7850449, 7850449, 7850449, 1526171, 68185267, 3429883, 3429883

Offset: 0

Author

David W. Wilson, Nov 18 2013

Keywords

• nonn
• frac

Comments

Sequence A231692 includes a proof that a(n) is never 0 for n > 1.

Examples

			1-1/2-1/3-1/4+1/5 = 7/60. No other choice of term signs yields a smaller nonnegative fraction, so a(5) = 7.
0/1, 1/1, 1/2, 1/6, 1/12, 7/60, 1/20, 11/420, 13/840, 11/2520, 11/2520, 23/27720, 23/27720, 607/360360, 251/360360, 251/360360, 25/144144, 97/12252240, ...
		

Crossrefs

Cf. A232112 (denominators), A231692.

Programs

Mathematica

nMax = 19; d = {0}; Table[d = Flatten[{d + 1/n, d - 1/n}]; Numerator[Min[Abs[d]]], {n, nMax}] (* T. D. Noe, Nov 20 2013 *)

PARI

a(n,t=0)=if(n==1,numerator(abs(n-t)),min(a(n-1,t-1/n),a(n-1,t+1/n))) \\ Charles R Greathouse IV, Apr 06 2014

Python

from itertools import product
from fractions import Fraction
def A232111(n): return min(x for x in (sum(d[i]*Fraction(1,i+1) for i in range(n)) for d in product((1,-1),repeat=n)) if x >= 0).numerator # Chai Wah Wu, Nov 24 2021