%I #5 Apr 28 2014 18:39:11
%S 3,4,10,12,25,545,589,2075,4883,7999,23074,31672,41958,904492,1356678,
%T 2738806,2774896,53721092,226271724,3775956307,15100042131,66836971558
%N Numbers n such that log(n!) is closer to an integer than is log(m!) for any m with 2<m<n.
%C a(k)! is the closest factorial to exp(A101507(k)). The next term is > 10^11.
%e a(1)=3 because log(3!)=1.79176 is closer to 2 than is log(2!)=0.693147 to 1.
%e a(2)=4: log(4!)=3.178054, a(3)=10: log(10!)=15.1044126, a(4)=12: log(12!)=19.987214, a(5)=25: log(25!)=58.003605.
%o (PARI) r=9;for(n=4,1e7,t=lngamma(n);t=abs(t-round(t)); if(t<r,r=t;print1(n-1", "))) \\ _Charles R Greathouse IV_, Apr 28 2014
%Y Cf. A101507, A046654 nearest integer to Sum_{k=1..n} log(k).
%K more,nonn
%O 1,1
%A _Hugo Pfoertner_, Dec 20 2004
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