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%I #23 Jun 18 2021 12:15:33
%S 1,3,0,4,3,5,1,1,7,8,9,0,1,0,3,6,5,3,3,6,4,7,2,0,1,2,3,1,4,8,6,2,3,4,
%T 0,7,5,0,3,5,5,3,3,8,2,9,9,8,9,0,2,3,1,7,9,8,1,7,3,3,2,0,9,5,6,8,8,9,
%U 1,5,0,9,3,2,8,7,5,7,1,2,2,1,0,0,0,4,8
%N Decimal expansion of the solution to x^x = sqrt(2).
%F Equals log(2)/(2*LambertW(log(2)/2)). - _Alois P. Heinz_, Jun 02 2021
%e 1.304351178901036533647201231486234...
%t RealDigits[Log[Sqrt[2]]/ProductLog[Log[Sqrt[2]]], 10, 100][[1]] (* _Amiram Eldar_, Jun 02 2021 *)
%t RealDigits[x/.FindRoot[x^x==Sqrt[2],{x,1},WorkingPrecision-> 120],10,120][[1]] (* _Harvey P. Dale_, Jun 18 2021 *)
%o (PARI) solve(x=1,2,x^x-sqrt(2)) \\ _Hugo Pfoertner_, Jun 02 2021
%Y Cf. A030798.
%K cons,nonn
%O 1,2
%A _Christoph B. Kassir_, Jun 01 2021
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