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

1,1

Links

Table of n, a(n) for n=1..120.

Eric Weisstein's World of Mathematics, e

Eric Weisstein's World of Mathematics, Nested Radical

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/...))))))))).

Example

3.495854711908497636885040848013394528609516258957759538...

Mathematica

RealDigits[Sqrt[E] ((Sqrt[E] + Sqrt[E + 4])/2), 10, 120][[1]]

Prog

(PARI) exp(1)/2+sqrt(4*exp(1)+exp(2))/2 \\ Charles R Greathouse IV, Apr 20 2016
(PARI) t=exp(.5); t*(t+sqrt(exp(1)+4))/2 \\ Charles R Greathouse IV, Apr 20 2016

Crossrefs

Cf. A001113, A019774, A100943, A189970, A268580.

Sequence in context: A190285 A276521 A247567 * A070154 A331025 A330403

Adjacent sequences: A271526 A271527 A271528 * A271530 A271531 A271532

Keyword

nonn,cons

Author

Ilya Gutkovskiy, Apr 09 2016

Status

approved