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A174968 Decimal expansion of (1 + sqrt(2))/2. 13
1, 2, 0, 7, 1, 0, 6, 7, 8, 1, 1, 8, 6, 5, 4, 7, 5, 2, 4, 4, 0, 0, 8, 4, 4, 3, 6, 2, 1, 0, 4, 8, 4, 9, 0, 3, 9, 2, 8, 4, 8, 3, 5, 9, 3, 7, 6, 8, 8, 4, 7, 4, 0, 3, 6, 5, 8, 8, 3, 3, 9, 8, 6, 8, 9, 9, 5, 3, 6, 6, 2, 3, 9, 2, 3, 1, 0, 5, 3, 5, 1, 9, 4, 2, 5, 1, 9, 3, 7, 6, 7, 1, 6, 3, 8, 2, 0, 7, 8, 6, 3, 6, 7, 5, 0 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) is the diameter of the circle around the Vitruvian Man when the square has sides of unit length. See illustration in links. - Kival Ngaokrajang, Jan 29 2015

The iterated function z^2 - 1/4, starting from z = 0, gives a pretty good rational approximation of (-1)((1 + sqrt(2))/2 - 1) to more than eight decimal digits after just twenty steps. - Alonso del Arte, Apr 09 2016

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000

Kival Ngaokrajang, Illustration of Vitruvian Man and construction rule

Wikipedia, Vitruvian Man

EXAMPLE

(1 + sqrt(2))/2 = 1.20710678118654752440...

MATHEMATICA

First@RealDigits[(1 + Sqrt[2])/2, 10, 105] (* Michael De Vlieger, Jan 29 2015 *)

PROG

(PARI) (1+sqrt(2))/2 \\ Altug Alkan, Apr 16 2016

CROSSREFS

Cf. A002193 (decimal expansion of sqrt(2)), A010685 (continued fraction expansion of (1 + sqrt(2))/2), A249403.

Sequence in context: A192496 A156442 A268683 * A254445 A346670 A140663

Adjacent sequences:  A174965 A174966 A174967 * A174969 A174970 A174971

KEYWORD

cons,nonn,easy

AUTHOR

Klaus Brockhaus, Apr 02 2010

STATUS

approved

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Last modified May 27 07:25 EDT 2022. Contains 354093 sequences. (Running on oeis4.)