

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
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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. 6162.


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



