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A296301 Decimal expansion of Product_{k>=2} k^(1/k!).

%I A296301 #22 Feb 16 2025 08:33:52
%S A296301 1,8,2,9,0,2,4,6,7,9,5,6,3,5,7,1,8,6,4,3,8,9,5,7,2,3,5,7,3,6,4,8,8,5,
%T A296301 8,4,9,1,0,0,7,6,7,6,3,3,3,7,2,1,1,4,1,1,6,7,3,0,6,4,4,1,2,4,6,1,9,7,
%U A296301 0,1,8,2,5,3,1,0,1,2,8,6,0,3,4,9,7,4,9,7,2,5,5,9,4,6,8,0,7,4,7
%N A296301 Decimal expansion of Product_{k>=2} k^(1/k!).
%H A296301 G. C. Greubel, <a href="/A296301/b296301.txt">Table of n, a(n) for n = 1..5000</a>
%H A296301 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/NestedRadical.html">Nested Radical</a>
%H A296301 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SomossQuadraticRecurrenceConstant.html">Somos's Quadratic Recurrence Constant</a>
%F A296301 Equals (2*(3*(4*(5*(6*(7*...)^(1/7))^(1/6))^(1/5))^(1/4))^(1/3))^(1/2).
%F A296301 Equals exp(Sum_{k>=2} log(k)/k!).
%F A296301 Equals lim_{k->infinity} b(k)^(1/k!), where b(k) = k*b(k-1)^k with b(0) = 1.
%F A296301 Equals Product_{p prime} p^(Sum_{k>=2} (p-adic valuation of k)/k!).
%e A296301 1.8290246795635718643895723573648858491007676333721141167306441...
%t A296301 RealDigits[Exp[Sum[ Log[k]/k!, {k, 2, 700}]], 10, 100][[1]] (* _G. C. Greubel_, Jul 28 2018 *)
%o A296301 (PARI) exp(suminf(k=2, log(k)/k!)) \\ _Michel Marcus_, Dec 11 2017
%Y A296301 Cf. A112302, A115522, A123852, A188835, A259235.
%K A296301 nonn,cons
%O A296301 1,2
%A A296301 _Ilya Gutkovskiy_, Dec 09 2017