

A143300


Decimal expansion of the GohSchmutz constant.


2



1, 1, 1, 7, 8, 6, 4, 1, 5, 1, 1, 8, 9, 9, 4, 4, 9, 7, 3, 1, 4, 0, 4, 0, 9, 9, 6, 2, 0, 2, 6, 5, 6, 5, 4, 4, 4, 1, 6, 3, 1, 1, 5, 5, 1, 2, 0, 4, 1, 2, 8, 8, 4, 2, 6, 5, 0, 6, 2, 8, 6, 5, 1, 4, 0, 1, 6, 0, 5, 4, 5, 5, 1, 8, 4, 2, 0, 3, 8, 5, 9, 1, 8, 1, 4, 8, 8, 0, 0, 7, 3, 5, 6, 5, 0, 0, 5, 2, 7, 1, 2, 9, 1, 2, 7
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OFFSET

1,4


COMMENTS

This constant is the limit of the logarithm expected order of a random permutation of length n, divided by sqrt(n/log n). In other words, log(A060014(n)/n!) ~ c sqrt(n/log n) where c is this constant. Stong improves the error term to O(sqrt(n) log log n/log n).  Charles R Greathouse IV, Nov 06 2014


LINKS

Table of n, a(n) for n=1..105.
P. Erdős and P. Turán, On some problems of a statistical group theory, IV, Acta Math. Acad. Sci. Hungar. 19 (1968), pp. 413435. [alternate link]
William M. Y. Goh and Eric Schmutz, The expected order of a random permutation, Bulletin of the London Mathematical Society 23:1 (1991), pp. 3442.
Richard Stong, The average order of a permutation, Electronic Journal of Combinatorics 5 (1998), 6 pp.
Eric Weisstein's World of Mathematics, GohSchmutz Constant


EXAMPLE

1.1178641511899449731...


MATHEMATICA

RealDigits[ N[ Integrate[Log[1 + t]/(E^t  1), {t, 0, Infinity}], 105]][[1]] (* JeanFrançois Alcover, Oct 26 2012 *)


PROG

(PARI) intnum(t=0, [oo, 1], log(1+t)/(exp(t)1)) \\ Charles R Greathouse IV, Nov 05 2014


CROSSREFS

Sequence in context: A004496 A197762 A181624 * A242816 A093827 A245736
Adjacent sequences: A143297 A143298 A143299 * A143301 A143302 A143303


KEYWORD

nonn,cons


AUTHOR

Eric W. Weisstein, Aug 05, 2008


STATUS

approved



