A061195 Minimum positive numerator of s_1/1 + ... + s_n/n in lowest terms, where each s_i equals 1 or -1.

1, 1, 1, 1, 7, 1, 11, 9, 11, 11, 23, 23, 607, 251, 59, 25, 97, 97, 2647, 2647, 1337, 457, 8917, 8917, 7951, 4261, 12439, 12439, 587971, 587971, 9687661, 13828799, 505163, 1554793, 1554793, 1554793, 1526171

Offset

1,5

Links

Table of n, a(n) for n=1..37.

Example

1/1 - 1/2 - 1/3 + 1/4 - 1/5 - 1/6 = 1/20, so a(6)=1.

Mathematica

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

Prog

(PARI) a(n) = {lcmn = 1; for (i=1, n, lcmn = lcm(i, lcmn)); minn = lcmn; for (i=0, 2^(n-1)-1, b = binary(i); while (#b != n, b = concat(0, b); ); num = numerator(abs(sum(ii = 1, n, (-1)^b[ii]/ii))); minn = min(minn, num); ); return(minn); } \\ Michel Marcus, Jun 15 2013

Crossrefs

Cf. A061194.

Cf. A232090 (minimal possible denominator).

Sequence in context: A349140 A178034 A124886 * A232111 A074283 A331337

Adjacent sequences: A061192 A061193 A061194 * A061196 A061197 A061198

Keyword

nonn

Author

Greg Martin (gerg(AT)math.toronto.edu), Apr 19 2001

Extensions

More terms from Naohiro Nomoto, Jun 24 2001

a(22)-a(25) from Zak Seidov, Nov 20 2013

a(26)-a(33) from Zak Seidov, Nov 24 2013

a(34)-a(37) from Giovanni Resta, Jun 12 2016

Status

approved