A267141 Number of weeks in n! seconds, for n >= 10.

6, 66, 792, 10296, 144144, 2162160, 34594560, 588107520, 10585935360, 201132771840, 4022655436800, 84475764172800, 1858466811801600, 42744736671436800, 1025873680114483200, 25646842002862080000, 666817892074414080000

Offset

10,1

Comments

10! seconds = 6 weeks (exactly)

11! seconds = 66 weeks (exactly)

12! seconds = 792 weeks (exactly), etc.

Demonstration of first term:

6 w * 7 d/w * 24 h/d * 60 m/h * 60 s/m = seconds in 6 weeks =

(2*3)*(1*7) *(3*8) * (6*10) * (3*5*4) =

1*2*3*4*5*6*7*8*(3^2)*10 = 10! seconds

Links

Table of n, a(n) for n=10..26.

Brady Haran, James Grime, 10!, Numberphile video (2012)

Formula

a(n) = 6*n!/10!.

a(n) = 6*A051431(n-10), for n>=10.

Example

For n=12, a(12) = 6*(12)!/10! = 792; interpretation: 12! seconds = 792 weeks.

Mathematica

f[n_] := n!/(60*60*24*7); Array[f, 17, 10] (* Robert G. Wilson v, Jan 12 2016 *)

Prog

(PARI) a(n) = 6*n!/10!; \\ Altug Alkan, Jan 12 2016

Crossrefs

Cf. A051431.

Sequence in context: A127857 A127858 A173535 * A004355 A282046 A124862

Adjacent sequences: A267138 A267139 A267140 * A267142 A267143 A267144

Keyword

easy,nonn

Author

Richard H. Sweetman, Jan 10 2016

Status

approved