

A101506


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


2



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

1,1


COMMENTS

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


LINKS

Table of n, a(n) for n=1..22.


EXAMPLE

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.


PROG

(PARI) r=9; for(n=4, 1e7, t=lngamma(n); t=abs(tround(t)); if(t<r, r=t; print1(n1", "))) \\ Charles R Greathouse IV, Apr 28 2014


CROSSREFS

Cf. A101507, A046654 nearest integer to Sum_{k=1..n} log(k).
Sequence in context: A135116 A259559 A050187 * A092434 A239632 A031367
Adjacent sequences: A101503 A101504 A101505 * A101507 A101508 A101509


KEYWORD

more,nonn


AUTHOR

Hugo Pfoertner, Dec 20 2004


STATUS

approved



