Here is some data on the partial sums (with the convention
when
) for small values of
.
Here is a plot for (click to enlarge)
The final values at have some noticeable structure:
firstly, all values of which are a multiple of
are positive while the rest are negative (at least for
).
then there are some exact results (accidental ones maybe?), denoting by its index
we have:
,
,
,
,
.
k;
1;-259
2;-268
3;239
4;-256
5;-107
6;178
7;-95
8;-178
9;363
10;-160
11;-107
12;210
13;-111
14;-100
15;219
16;-164
17;-181
18;438
19;-193
20;-210
21;303
22;-126
23;-149
24;254
25;-155
26;-184
27;453
28;-164
29;-139
30;236
31;-139
32;-122
33;217
34;-166
35;-107
36;418
37;-195
38;-120
39;219
Tags: polymath5
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