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%I #11 Aug 09 2021 14:02:14
%S 1,1,9,0,7,8,3,6,8,2,9,7,3,2,9,5,9,1,5,3,1,8,0,0,2,5,0,6,8,5,8,5,7,0,
%T 1,0,1,7,3,3,5,7,2,6,5,9,1,9,2,2,8,4,2,6,7,1,3,7,1,5,2,4,4,3,0,2,6,6,
%U 5,0,3,8,9,6,7,2,9,8,7,5,9,3,4,9,2,1,0,0,9,3,7,7,2,2,0,3,3,3,7,2,9,6
%N Decimal expansion of the number x satisfying x*2^x=e.
%e x=1.19078368297329591531800250685857010...
%t Plot[{2^x, 1/x, 2/x, 3/x, 4/x}, {x, 0, 2}]
%t t = x /. FindRoot[2^x == 1/x, {x, 0.5, 1}, WorkingPrecision -> 100]
%t RealDigits[t] (* A104748 *)
%t t = x /. FindRoot[2^x == E/x, {x, 0.5, 1}, WorkingPrecision -> 100]
%t RealDigits[t] (* A196549 *)
%t t = x /. FindRoot[2^x == 3/x, {x, 0.5, 2}, WorkingPrecision -> 100]
%t RealDigits[t] (* A196550 *)
%t t = x /. FindRoot[2^x == 4/x, {x, 0.5, 2}, WorkingPrecision -> 100]
%t RealDigits[t] (* A196551 *)
%t t = x /. FindRoot[2^x == 5/x, {x, 0.5, 2}, WorkingPrecision -> 100]
%t RealDigits[t] (* A196552 *)
%t t = x /. FindRoot[2^x == 6/x, {x, 0.5, 2}, WorkingPrecision -> 100]
%t RealDigits[t] (* A196553 *)
%t RealDigits[ ProductLog[ E*Log[2] ] / Log[2], 10, 100] // First (* _Jean-François Alcover_, Feb 27 2013 *)
%Y Cf. A196515.
%K nonn,cons
%O 1,3
%A _Clark Kimberling_, Oct 03 2011
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