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A238695 Decimal expansion of Product_{k>=0} (1+1/k!).

%I A238695 #42 Aug 27 2025 05:18:23
%S A238695 7,3,6,4,3,0,8,2,7,2,3,6,7,2,5,7,2,5,6,3,7,2,7,7,2,5,0,9,6,3,1,0,5,3,
%T A238695 0,9,5,6,5,4,2,5,6,8,3,6,0,6,8,9,0,7,6,6,0,7,9,2,5,5,4,9,5,3,6,9,6,2,
%U A238695 3,8,1,6,4,4,0,7,6,2,3,9,8,1,9,8,1,4,0,5,0,5,6,3,7,1,4,8,1,7,9,0,3,2,7,2,4,9,3,9,5,7,4,5,6,0,2,1
%N A238695 Decimal expansion of Product_{k>=0} (1+1/k!).
%C A238695 Conjectured to be irrational, transcendental and normal, none have been shown. Product is sometimes taken from n=1, leading to half the stated value.
%H A238695 Lucian Craciun, <a href="/A238695/b238695.txt">Table of n, a(n) for n = 1..10000</a>
%H A238695 StackExchange, <a href="http://math.stackexchange.com/questions/352973">Is Product_{n>=0} (1+1/n!) = e^2?</a>, Apr 06 2013
%H A238695 StackExchange, <a href="http://math.stackexchange.com/questions/460579">How to compute Product_{n>=1} (1+1/n!)?</a>, Aug 05 2013
%H A238695 Wolfram Alpha, <a href="http://www.wolframalpha.com/input/?i=\prod_{n%3D0}^{\infty}+(1%2B\frac{1}{n!})">Product_{n>=0} (1+1/n!)</a>
%e A238695 7.3643082723672572563727725096310530956542568360689...
%p A238695 evalf(product(1+1/n!, n = 0..infinity), 100) # _Lucian Craciun_, Feb 17 2017
%t A238695 RealDigits[Product[1+1/n!, {n, 0, 75}], 10, 106][[1]] (* _Robert G. Wilson v_, Mar 19 2014 *)
%o A238695 (PARI) prodinf(n=1,1+1/gamma(n)) \\ _Charles R Greathouse IV_, Nov 13 2014
%Y A238695 Cf. A072334, A217757, A282529.
%Y A238695 Cf. A387175 (continued fraction).
%K A238695 nonn,cons,changed
%O A238695 1,1
%A A238695 _Frederick Reckless_, Mar 03 2014
%E A238695 Added more digits from b-file, so as to cover exactly three full rows of text. - _Lucian Craciun_, Feb 22 2017