A232112 Denominator of smallest nonnegative fraction of form +- 1 +- 1/2 +- 1/3 ... +- 1/n.

1, 1, 2, 6, 12, 60, 20, 420, 840, 2520, 2520, 27720, 27720, 360360, 360360, 360360, 144144, 12252240, 12252240, 232792560, 232792560, 232792560, 46558512, 5354228880, 5354228880, 2974571600, 26771144400, 80313433200

Offset: 0

Author

David W. Wilson, Nov 18 2013

Keywords

• nonn
• frac

Comments

Numerators are A232111.

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) = 60.
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, ...
		

Links

• David W. Wilson, Table of n, a(n) for n = 0..40

Crossrefs

Cf. A232111.

Programs

Mathematica

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

PARI

a(n,t=0)=if(n==1,denominator(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 math import lcm, gcd
from itertools import product
def A232112(n):
    if n <= 1: return 1
    m = lcm(*range(2,n+1))
    mtuple = tuple(m//i for i in range(2,n+1))
    return m//gcd(m,min(abs(m+sum(d[i]*mtuple[i] for i in range(n-1))) for d in product((-1,1),repeat=n-1))) # Chai Wah Wu, Nov 25 2021