A061195 -id:A061195 - cp's OEIS frontend

A232090 Minimal possible denominator for a sum of the form 1 +/- 1/2 +/- 1/3 +/- ... +/- 1/n.

1, 2, 6, 12, 60, 20, 140, 280, 2520, 2520, 27720, 27720, 360360, 360360, 72072, 144144, 2450448, 272272, 5173168, 5173168, 739024, 739024, 16997552, 16997552, 424938800, 424938800, 11473347600, 11473347600, 332727080400, 332727080400

Offset: 1

M. F. Hasler, Nov 18 2013

nonn

Differs from A203811 from a(18)=272272 on, and from A002805 and A231693 from a(15)=72072 on.

Giovanni Resta, Table of n, a(n) for n = 1..37
F. T. Adams-Watters, Re: Reciprocal Recaman, SeqFan list, Nov 17 2013

Cf. A061195 (minimal possible positive numerator).

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

for(n=0,19,m=(n+1)!;for(k=0,2^n-1,m=min(denominator(sum(j=2,n+1,(-1)^bittest(k,j-2)/j,1)),m));print1(m","))

Terms a(21)-a(30) from David W. Wilson, Nov 19 2013

A061194 Minimum positive value of lcm{1,...,n}*(s_1/1 + ... + s_n/n), where each s_i equals 1 or -1.

Original entry on oeis.org

1, 1, 1, 1, 7, 3, 11, 13, 11, 11, 23, 23, 607, 251, 251, 125, 97, 97, 3767, 3767, 3767, 2285, 24319, 24319, 71559, 4261, 13703, 13703, 872843, 872843, 17424097, 13828799, 902339, 7850449, 7850449, 7850449, 10683197, 68185267, 37728713, 37728713, 740674333

Offset: 1

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

nonn

Nonnegative by considering the largest power of 2 up to n.

			1/1 - 1/2 - 1/3 - 1/4 - 1/5 + 1/6 + 1/7 = 11/420 = 11/lcm(1,2,3,4,5,6,7), so a(7) <= 11; no other choice of signs yields 1/420, ..., 10/420, so a(7)=11.

A231606 Maximal possible numerator for a sum of the form 1 +/- 1/2 +/- 1/3 +/- ... +/- 1/n.

Original entry on oeis.org

1, 3, 11, 25, 137, 127, 949, 2003, 7129, 7381, 83711, 86021, 1145993, 1171733, 1195757, 2436559, 42142223, 41461543, 800021557, 788381929, 799467289, 810048769, 18863914247, 19087007117, 99182995801, 100212655201, 312536252003, 315404588903

Offset: 1

T. D. Noe, Nov 19 2013

nonn

Cf. A003418 (maximal denominator).

Cf. A061195 (minimal numerator), A232090 (minimal denominator).

nMax = 19; d = {0}; Table[d = Flatten[{d + 1/n, d - 1/n}]; Max[Abs[Numerator[d]]], {n, nMax}]

cp's OEIS Frontend

A232090 Minimal possible denominator for a sum of the form 1 +/- 1/2 +/- 1/3 +/- ... +/- 1/n.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Extensions

A061194 Minimum positive value of lcm{1,...,n}*(s_1/1 + ... + s_n/n), where each s_i equals 1 or -1.

Views

Author

Keywords

Comments

Examples

Crossrefs

Extensions

A231606 Maximal possible numerator for a sum of the form 1 +/- 1/2 +/- 1/3 +/- ... +/- 1/n.

Views

Author

Keywords

Crossrefs

Programs

Mathematica