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A068460 Factorial expansion of log(7) = Sum_{n>=1} a(n)/n!.

%I A068460 #19 May 22 2022 09:49:09
%S A068460 1,1,2,2,3,3,0,3,0,8,8,2,11,1,5,11,1,7,1,11,16,12,12,13,5,4,26,19,12,
%T A068460 20,0,18,14,22,6,29,0,27,16,23,23,23,34,27,4,27,18,0,10,27,42,24,9,16,
%U A068460 6,52,2,38,44,30,51,61,7,19,0,45,18,51,43,54,7,15,69,44,51,9,74,5,69
%N A068460 Factorial expansion of log(7) = Sum_{n>=1} a(n)/n!.
%H A068460 G. C. Greubel, <a href="/A068460/b068460.txt">Table of n, a(n) for n = 1..10000</a>
%H A068460 <a href="https://oeis.org/index/Fa#facbase">Index entries for factorial base representation of noninteger constants</a>
%e A068460 log(7) = 1 + 1/2! + 2/3! + 2/4! + 3/5! + 3/6! + 0/7! + 3/8! + 0/9! + ...
%p A068460 Digits:=200: a:=n->`if`(n=1,floor(log(7)),floor(factorial(n)*log(7))-n*floor(factorial(n-1)*log(7))); seq[120](a(n),n=1..80); # _Muniru A Asiru_, Dec 06 2018
%t A068460 With[{b = Log[7]}, Table[If[n == 1, Floor[b], Floor[n!*b] - n*Floor[(n - 1)!*b]], {n, 1, 100}]] (* _G. C. Greubel_, Dec 05 2018 *)
%o A068460 (PARI) vector(30,n,if(n>1,t=t%1*n,t=log(7))\1) \\ Increase realprecision (e.g., \p500) to compute more terms. - _M. F. Hasler_, Nov 25 2018
%o A068460 (PARI) default(realprecision, 250); b = log(7); 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 A068460 (Magma) SetDefaultRealField(RealField(250));  [Floor(Log(7))] cat [Floor(Factorial(n)*Log(7)) - n*Floor(Factorial((n-1))*Log(7)) : n in [2..80]]; // _G. C. Greubel_, Dec 05 2018
%o A068460 (Sage)
%o A068460 def a(n):
%o A068460     if (n==1): return floor(log(7))
%o A068460     else: return expand(floor(factorial(n)*log(7)) - n*floor(factorial(n-1)*log(7)))
%o A068460 [a(n) for n in (1..80)] # _G. C. Greubel_, Dec 05 2018
%Y A068460 Cf. A016630 (decimal expansion), A016735 (continued fraction).
%Y A068460 Cf. A067882 (log(2)), A322334 (log(3)), A322333 (log(5)), A068461 (log(11)).
%K A068460 nonn
%O A068460 1,3
%A A068460 _Benoit Cloitre_, Mar 10 2002
%E A068460 Name edited and keywords cons,easy removed by _M. F. Hasler_, Nov 25 2018