Jon A. Wellner

Values of L_n, the length of the longest increasing subsequence 
in 10^4 random permutations of {1, 2, ... , n}  for n=4x10^6.
There was 1 permutation for which L_n was 3934, 1 for which 
it was 3938, and so forth.

1     3934
1     3938
2     3944
4     3945
2     3946
3     3947
14    3948
3     3949
6     3950
12    3951
17    3952
32    3953
39    3954
36    3955
41    3956
73    3957
76    3958
71    3959
93    3960
101   3961
130   3962
134   3963
145   3964
180   3965
223   3966
215   3967
290   3968
262   3969
285   3970
346   3971
323   3972
357   3973
318   3974
352   3975
366   3976
338   3977
379   3978
334   3979
321   3980
341   3981
324   3982
286   3983
308   3984
274   3985
276   3986
248   3987
231   3988
206   3989
186   3990
175   3991
153   3992
153   3993
121   3994
121   3995
110   3996
88    3997
69    3998
60    3999
67    4000
57    4001
39    4002
30    4003
24    4004
17    4005
21    4006
11    4007
12    4008
13    4009
8     4010
8     4011
4     4012
9     4013
3     4014
5     4015
7     4016
3     4017
2     4018
1     4019
2     4020
1     4023
1     4024