

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
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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

Table of n, a(n) for n=1..17.
Stefan Kraemer, Euler's Constant 0.577... Its Mathematics and History
D. H. Lehmer, Euler constants for arithmetic progressions, Acta Arith. 27 (1975) 125142.


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

Sequence in context: A285084 A248187 A190772 * A306777 A062891 A018599
Adjacent sequences: A130670 A130671 A130672 * A130674 A130675 A130676


KEYWORD

nonn,uned


AUTHOR

Stefan Krämer, Jun 28 2007


STATUS

approved



