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 A139339 Decimal expansion of the square root of the golden ratio. 26
 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. - 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 = sqrt((1 + sqrt(5))/2). EXAMPLE c = 1.2720196495140689642524224617374914917156080418400... MAPLE Digits:=100: evalf(sqrt((1+sqrt(5))/2)); # Muniru A Asiru, Sep 11 2018 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 15 09:05 EST 2019. Contains 329995 sequences. (Running on oeis4.)