|
%I #25 Jun 16 2018 15:59:10
%S 6,66,792,10296,144144,2162160,34594560,588107520,10585935360,
%T 201132771840,4022655436800,84475764172800,1858466811801600,
%U 42744736671436800,1025873680114483200,25646842002862080000,666817892074414080000
%N Number of weeks in n! seconds, for n >= 10.
%C 10! seconds = 6 weeks (exactly)
%C 11! seconds = 66 weeks (exactly)
%C 12! seconds = 792 weeks (exactly), etc.
%C Demonstration of first term:
%C 6 w * 7 d/w * 24 h/d * 60 m/h * 60 s/m = seconds in 6 weeks =
%C (2*3)*(1*7) *(3*8) * (6*10) * (3*5*4) =
%C 1*2*3*4*5*6*7*8*(3^2)*10 = 10! seconds
%H Brady Haran, James Grime, <a href="https://www.youtube.com/watch?v=kUBIJdGsD1A">10!</a>, Numberphile video (2012)
%F a(n) = 6*n!/10!.
%F a(n) = 6*A051431(n-10), for n>=10.
%e For n=12, a(12) = 6*(12)!/10! = 792; interpretation: 12! seconds = 792 weeks.
%t f[n_] := n!/(60*60*24*7); Array[f, 17, 10] (* _Robert G. Wilson v_, Jan 12 2016 *)
%o (PARI) a(n) = 6*n!/10!; \\ _Altug Alkan_, Jan 12 2016
%Y Cf. A051431.
%K easy,nonn
%O 10,1
%A _Richard H. Sweetman_, Jan 10 2016
| 