|
|
A130673
|
|
Smallest m of r=1,2,3,... where the generalized Euler constants (of D. H. Lehmer) E(r,m) change their sign: E(r,m) > 0 and E(r+1,m) < 0.
|
|
0
|
|
|
2, 3, 6, 9, 13, 17, 21, 25, 29, 34, 39, 43, 48, 53, 58, 63, 68
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Maple produces the following table:
...m................|..r
...2,...............|..1
...3,.4,.5..........|..2
...6,.7,.8..........|..3
...9,10,11,12.......|..4
..13,14,15,16.......|..5
..17,18,19,20.......|..6
..21,22,23,24.......|..7
..25,26,27,28.......|..8
..29,30,31,32,33....|..9
..34,35,36,37,38....|.10
..39,40,41,42.......|.11
..43,44,45,46,47....|.12
..48,49,50,51,52....|.13
..53,54,55,56,57....|.14
..58,59,60,61,62....|.15
..63,64,65,66,67....|.16
..68,69,70,71,72,73.|.17
|
|
REFERENCES
|
Stefan Kraemer, Eulers constant and related numbers, preprint, 2005.
|
|
LINKS
|
|
|
FORMULA
|
E(r,m) = lim_{n->oo} (H_{r,m}(n) - log n / m); E(r,m) = -1/m * (log m + Psi(r/m))
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,uned
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|