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A067881 Factorial expansion of sqrt(3) = Sum_{n>=1} a(n)/n!.

%I A067881 #22 May 22 2022 09:49:01
%S A067881 1,1,1,1,2,5,0,4,2,5,10,8,1,5,6,8,5,13,18,0,7,20,9,6,14,2,7,7,18,11,0,
%T A067881 12,20,10,31,28,27,34,29,18,13,8,28,14,9,12,39,5,15,8,5,0,7,21,54,13,
%U A067881 16,20,24,18,12,14,6,53,21,42,47,14,46,14,42,71,41,63,24,28,32,61,35
%N A067881 Factorial expansion of sqrt(3) = Sum_{n>=1} a(n)/n!.
%H A067881 G. C. Greubel, <a href="/A067881/b067881.txt">Table of n, a(n) for n = 1..10000</a>
%H A067881 <a href="https://oeis.org/index/Fa#facbase">Index entries for factorial base representation</a>
%F A067881 a(1) = 1; for n > 1, a(n) = floor(n!*sqrt(3)) - n*floor((n-1)!*sqrt(3)).
%e A067881 sqrt(3) = 1 + 1/2! + 1/3! + 1/4! + 2/5! + 5/6! + 0/7! + 4/8! + 2/9! + ...
%p A067881 Digits:=200: a:=n->`if`(n=1,floor(sqrt(3)),floor(factorial(n)*sqrt(3))-n*floor(factorial(n-1)*sqrt(3))): seq(a(n),n=1..90); # _Muniru A Asiru_, Dec 11 2018
%t A067881 With[{b = Sqrt[3]}, Table[If[n == 1, Floor[b], Floor[n!*b] - n*Floor[(n - 1)!*b]], {n, 1, 100}]] (* _G. C. Greubel_, Dec 10 2018 *)
%o A067881 (PARI) default(realprecision, 250); {b = sqrt(3); a(n) = if(n==1, floor(b), floor(n!*b) - n*floor((n-1)!*b))};
%o A067881 for(n=1, 80, print1(a(n), ", ")) \\ _G. C. Greubel_, Dec 10 2018
%o A067881 (PARI) apply( A067881(n)=if(n>1,sqrt(precision(3., n*log(n/2.5)\2.3+2))*(n-1)!%1*n\1,1), [1..79]) \\ _M. F. Hasler_, Dec 14 2018
%o A067881 (Magma) SetDefaultRealField(RealField(250));  [Floor(Sqrt(3))] cat [Floor(Factorial(n)*Sqrt(3)) - n*Floor(Factorial((n-1))*Sqrt(3)) : n in [2..80]]; // _G. C. Greubel_, Dec 10 2018
%o A067881 (Sage) b=sqrt(3);
%o A067881 def a(n):
%o A067881     if (n==1): return floor(b)
%o A067881     else: return expand(floor(factorial(n)*b) - n*floor(factorial(n-1)*b))
%o A067881 [a(n) for n in (1..80)] # _G. C. Greubel_, Dec 10 2018
%Y A067881 Cf. A002194 (decimal expansion), A040001 (continued fraction).
%Y A067881 Cf. A009949 (sqrt(2)), A068446 (sqrt(5)), A320839 (sqrt(7)).
%K A067881 easy,nonn
%O A067881 1,5
%A A067881 _Benoit Cloitre_, Mar 10 2002