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A209927 Decimal expansion of sqrt(3 + sqrt(3 + sqrt(3 + sqrt(3 + ... )))). 7
2, 3, 0, 2, 7, 7, 5, 6, 3, 7, 7, 3, 1, 9, 9, 4, 6, 4, 6, 5, 5, 9, 6, 1, 0, 6, 3, 3, 7, 3, 5, 2, 4, 7, 9, 7, 3, 1, 2, 5, 6, 4, 8, 2, 8, 6, 9, 2, 2, 6, 2, 3, 1, 0, 6, 3, 5, 5, 2, 2, 6, 5, 2, 8, 1, 1, 3, 5, 8, 3, 4, 7, 4, 1, 4, 6, 5, 0, 5, 2, 2, 2, 6, 0, 2, 3, 0, 9, 5, 4, 1, 0, 0, 9, 2, 4, 5, 3, 5, 8, 8, 3, 6, 7, 5, 7 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The number x given by the infinitely nested radical for n = 3 is such that x^2 = x + 3, bearing some similarity to the golden ratio phi with its property that phi^2 = phi + 1. Also, 3/x = x - 1.

LINKS

Table of n, a(n) for n=1..106.

FORMULA

Closed form: (sqrt(13) + 1)/2 = A098316-1 = A085550+2.

EXAMPLE

2.30277563773...

MATHEMATICA

RealDigits[(1 + Sqrt[13])/2, 10, 130][[1]]

RealDigits[ Fold[ Sqrt[#1 + #2] &, 0, Table[3, {n, 168}]], 10, 111][[1]] (* Robert G. Wilson v, Oct 02 2018 *)

PROG

(PARI) (sqrt(13)+1)/2 \\ Altug Alkan, Oct 03 2018

CROSSREFS

Cf. A157532 (continued fraction), A001622, A010470, A085550, A098316.

Sequence in context: A002392 A002708 A167925 * A059283 A160202 A195673

Adjacent sequences:  A209924 A209925 A209926 * A209928 A209929 A209930

KEYWORD

nonn,cons,easy

AUTHOR

Alonso del Arte, Mar 17 2012

STATUS

approved

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Last modified May 20 20:16 EDT 2019. Contains 323426 sequences. (Running on oeis4.)