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.

2, 3, 6, 9, 13, 17, 21, 25, 29, 34, 39, 43, 48, 53, 58, 63, 68

Offset: 1

Author

Stefan Krämer, Jun 28 2007

Keywords

• nonn
• uned

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

• Stefan Kraemer, Euler's Constant 0.577... Its Mathematics and History
• D. H. Lehmer, Euler constants for arithmetic progressions, Acta Arith. 27 (1975) 125-142.

Formula

E(r,m) = lim_{n->oo} (H_{r,m}(n) - log n / m); E(r,m) = -1/m * (log m + Psi(r/m))