A203812 Numbers n where abs(s(n)) produces a new minimum, with s(1) = 1 and s(i) = s(i-1) - sign(s(i-1))*(1/i).

1, 2, 3, 4, 6, 8, 10, 12, 14, 16, 18, 22, 30, 38, 54, 70, 118, 126, 134, 150, 166, 182, 198, 214, 246, 278, 374, 534, 598, 662, 790, 854, 982, 1110, 1238, 1366, 1494, 1622, 1878, 2006, 2134, 2390, 2902, 3158, 3670, 5462, 5974, 6486, 6998, 10070, 11094, 12118

Offset

1,2

Comments

Positions of decreasing minima of abs(A203810(i)/A203811(i)).

Links

Hugo Pfoertner, Table of n, a(n) for n = 1..131

Example

The first 4 fractions f(i)=A203810(i)/A203811(i) 1/1, 1/2, 1/6, -1/12 have decreasing absolute values. Therefore a(1)=1, a(2)=2, a(3)=3, a(4)=4. 5 is not in the sequence, because f(5)=7/60>1/12, but f(6)=-1/20 gives a(5)=6 because 1/20<1/12.
Fractions producing further decreasing absolute values are f(8)=-9/280, f(10)=-53/2520, f(12)=-373/27720, f(14)=-2869/360360, f(16)=-547/144144, f(18)=-1291/2450448, f(22)=-13913/232792560, f(30)=93259013/232908956280.

Prog

(PARI)
s=0; d=2; \
for (k=1, 12500, if(s>0, s-=1/k, s+=1/k); if(abs(s)<d, d=abs(s); print1(k, ", ")))
\\ Hugo Pfoertner, Nov 14 2017

Crossrefs

Cf. A203810, A203811.

Sequence in context: A064376 A283808 A068578 * A047894 A113769 A056865

Adjacent sequences: A203809 A203810 A203811 * A203813 A203814 A203815

Keyword

nonn

Author

Hugo Pfoertner and Rainer Rosenthal, Jan 06 2012

Status

approved