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Search: id:A130673
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| A130673 |
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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. |
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+0
1
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| 2, 3, 6, 9, 13, 17, 21, 25, 29, 34, 39, 43, 48, 53, 58, 63, 68
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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
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REFERENCES
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Stefan Kraemer, Eulers constant and related numbers, preprint, 2005.
D. H. Lehmer. Euler constants for arithmetical progressions. Acta Arithetica, vol.27, p. 125-142, 1975.
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LINKS
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Stefan Kraemer, Euler's Constant 0.577... Its Mathematics and History
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FORMULA
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E(r,m) = lim_{n->oo} (H_{r,m}(n) - log n / m); E(r,m) = -1/m * (log m + Psi(r/m))
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CROSSREFS
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Sequence in context: A058616 A123316 A096845 this_sequence A062891 A018599 A018347
Adjacent sequences: A130670 A130671 A130672 this_sequence A130674 A130675 A130676
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KEYWORD
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nonn,uned
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AUTHOR
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Stefan Kraemer (skraemer(AT)math.uni-goettingen.de), Jun 28 2007
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