%I #31 May 22 2022 09:49:12

%S 2,0,2,1,2,4,3,3,1,2,4,0,3,13,1,12,12,13,1,16,16,0,16,12,10,9,1,23,3,

%T 22,0,28,11,14,23,16,0,14,6,1,1,14,4,25,43,0,29,10,41,19,47,14,0,51,

%U 10,47,37,45,46,56,57,45,10,32,61,15,9,67,5,9,22,25,65,56,24,12,71,9,57

%N Factorial, or factoradic, expansion of log(11) = Sum_{n>=1} a(n)/n!, with a(n) as large as possible.

%H G. C. Greubel, <a href="/A068461/b068461.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="https://oeis.org/index/Fa#facbase">Index entries for factorial base representation of noninteger constants</a>

%e log(11) = 2 + 0/2! + 2/3! + 1/4! + 2/5! + 4/6! + 3/7! + 3/8! + 1/9! + ...

%t With[{b = Log[11]}, Table[If[n == 1, Floor[b], Floor[n!*b] - n*Floor[(n - 1)!*b]], {n, 1, 100}]] (* _G. C. Greubel_, Dec 05 2018 *)

%o (PARI) vector(30, n, if(n>1, t=t%1*n, t=log(11))\1) \\ Increase realprecision (e.g., \p500) to compute more terms. - _M. F. Hasler_, Nov 25 2018

%o (PARI) default(realprecision, 250); b = log(11); for(n=1, 80, print1(if(n==1, floor(b), floor(n!*b) - n*floor((n-1)!*b)), ", ")) \\ _G. C. Greubel_, Dec 05 2018

%o (Magma) SetDefaultRealField(RealField(250)); [Log(11)] cat [Floor(Factorial(n)*Log(11)) - n*Floor(Factorial((n-1))*Log(11)) : n in [2..80]]; // _G. C. Greubel_, Dec 05 2018

%o (Sage)

%o def a(n):

%o if n==1: return floor(log(11))

%o else: return expand(floor(factorial(n)*log(11)) - n*floor(factorial(n-1)*log(11)))

%o [a(n) for n in (1..80)] # _G. C. Greubel_, Dec 05 2018

%Y Cf. A016634 (decimal expansion), A016739 (continued fraction).

%Y Cf. A007514 vs. A075874 for factoradic expansion.

%Y Cf. A067882 (log(2)), A322334 (log(3)), A322333 (log(5)), A068460 (log(7)).

%K nonn

%O 1,1

%A _Benoit Cloitre_, Mar 10 2002

%E Name edited and keyword cons,easy removed by _M. F. Hasler_, Nov 26 2018