A101506 Numbers n such that log(n!) is closer to an integer than is log(m!) for any m with 2

3, 4, 10, 12, 25, 545, 589, 2075, 4883, 7999, 23074, 31672, 41958, 904492, 1356678, 2738806, 2774896, 53721092, 226271724, 3775956307, 15100042131, 66836971558

Offset: 1

Author

Hugo Pfoertner, Dec 20 2004

Keywords

• more
• nonn

Comments

a(k)! is the closest factorial to exp(A101507(k)). The next term is > 10^11.

Examples

			a(1)=3 because log(3!)=1.79176 is closer to 2 than is log(2!)=0.693147 to 1.
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.
		

Crossrefs

Cf. A101507, A046654 nearest integer to Sum_{k=1..n} log(k).

Programs

PARI

r=9;for(n=4,1e7,t=lngamma(n);t=abs(t-round(t)); if(tCharles R Greathouse IV, Apr 28 2014