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A139339 Decimal expansion of the square root of the golden ratio. 22
1, 2, 7, 2, 0, 1, 9, 6, 4, 9, 5, 1, 4, 0, 6, 8, 9, 6, 4, 2, 5, 2, 4, 2, 2, 4, 6, 1, 7, 3, 7, 4, 9, 1, 4, 9, 1, 7, 1, 5, 6, 0, 8, 0, 4, 1, 8, 4, 0, 0, 9, 6, 2, 4, 8, 6, 1, 6, 6, 4, 0, 3, 8, 2, 5, 3, 9, 2, 9, 7, 5, 7, 5, 5, 3, 6, 0, 6, 8, 0, 1, 1, 8, 3, 0, 3, 8, 4, 2, 1, 4, 9, 8, 8, 4, 6, 0, 2, 5, 8, 5, 3, 8, 5, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The hyperbolas x^2 - y^2 = 1 and xy = 1 meet at (c, 1/c) and (-c, -1/c), where c = sqrt(golden ratio); see the Mathematica program for a graph.  [From Clark Kimberling, Oct 19 2011]

An algebraic integer of degree 4. Minimal polynomial: x^4 - x^2 - 1. - Charles R Greathouse IV, Jan 07 2013

REFERENCES

Mohammad K. Azarian, Problem 123, Missouri Journal of Mathematical Sciences, Vol. 10, No. 3, Fall 1998, p. 176.  Solution published in Vol. 12, No. 1, Winter 2000, pp. 61-62.

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..10000

FORMULA

c = ((1 + sqrt(5))/2)^(1/2).

EXAMPLE

c = 1.2720196495140689642524224617374914917156080418400...

MATHEMATICA

N[Sqrt[GoldenRatio], 100]

FindRoot[x*Sqrt[-1 + x^2] == 1, {x, 1.2, 1.3}, WorkingPrecision -> 110]

Plot[{Sqrt[-1 + x^2], 1/x}, {x, 0, 3}] (* Clark Kimberling, Oct 19 2011 *)

PROG

(PARI) sqrt((1+sqrt(5))/2) \\ Charles R Greathouse IV, Jan 07 2013

CROSSREFS

Cf. A001622, A094214, A104457, A098317, A002390; A197762 (related intersection of hyperbolas).

Sequence in context: A242207 A060465 A219177 * A090986 A245221 A195726

Adjacent sequences:  A139336 A139337 A139338 * A139340 A139341 A139342

KEYWORD

nonn,cons,easy

AUTHOR

Mohammad K. Azarian, Apr 14 2008

STATUS

approved

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Last modified December 13 00:17 EST 2017. Contains 295954 sequences.