A271529 Decimal expansion of sqrt(e + e*sqrt(e + e*sqrt(e + ...))).
3, 4, 9, 5, 8, 5, 4, 7, 1, 1, 9, 0, 8, 4, 9, 7, 6, 3, 6, 8, 8, 5, 0, 4, 0, 8, 4, 8, 0, 1, 3, 3, 9, 4, 5, 2, 8, 6, 0, 9, 5, 1, 6, 2, 5, 8, 9, 5, 7, 7, 5, 9, 5, 3, 8, 1, 4, 1, 9, 2, 8, 9, 8, 1, 5, 0, 0, 9, 4, 1, 5, 4, 7, 7, 2, 2, 9, 0, 8, 1, 3, 3, 1, 7, 9, 2, 1, 2, 3, 4, 7, 8, 3, 3, 8, 9, 8, 4, 1, 7, 4, 3, 4, 4, 3, 0, 0, 7, 6, 1, 2, 2, 6, 1, 7, 5, 9, 2, 5, 7
Offset: 1
Examples
3.495854711908497636885040848013394528609516258957759538...
Links
- Eric Weisstein's World of Mathematics, e
- Eric Weisstein's World of Mathematics, Nested Radical
Programs
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Mathematica
RealDigits[Sqrt[E] ((Sqrt[E] + Sqrt[E + 4])/2), 10, 120][[1]]
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PARI
exp(1)/2+sqrt(4*exp(1)+exp(2))/2 \\ Charles R Greathouse IV, Apr 20 2016
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PARI
t=exp(.5); t*(t+sqrt(exp(1)+4))/2 \\ Charles R Greathouse IV, Apr 20 2016
Formula
Equals sqrt(e)*(sqrt(e) + sqrt(e + 4))/2.
Equals e + 1/(1 + 1/(e + 1/(1 + 1/(e + 1/(1 + 1/(e + 1/(1 + 1/(e + 1/(1 + 1/...))))))))).