OFFSET
1,3
COMMENTS
Continued fraction expansion of (5 + 3*sqrt(5))/10 is A010686.
The horizontal distance between the accumulation point and the outermost point of a golden spiral inscribed inside a golden rectangle with dimensions phi and 1 along the x and y axes, respectively (the vertical distance is A244847). - Amiram Eldar, May 18 2021
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 1.2 The Golden Mean, phi, p. 7.
LINKS
Muniru A Asiru, Table of n, a(n) for n = 1..1000 [a(1000) corrected by Georg Fischer, Apr 02 2020]
FORMULA
Equals (A134976 + 8)/10. - R. J. Mathar, Apr 12 2010
From Arkadiusz Wesolowski, Jan 07 2018: (Start)
Equals A001622^2 / sqrt(5).
Equals 1/A090550 + 1. - Michel Marcus, Apr 20 2020
Minimal polynomial is 5x^2 - 5x - 1 (this number is an algebraic number but not an algebraic integer). - Alonso del Arte, Apr 20 2020
Equals lim_{k->oo} Fibonacci(k+2)/Lucas(k). - Amiram Eldar, Feb 06 2022
EXAMPLE
(5 + 3*sqrt(5))/10 = 1.17082039324993690892...
MAPLE
Digits := 1000: (5+3*sqrt(5.0))/10; # Muniru A Asiru, Jan 22 2018
MATHEMATICA
RealDigits[(5 + 3 Sqrt[5])/10, 10, 1001][[1]] (* Georg Fischer, Apr 02 2020 *)
PROG
(Magma) SetDefaultRealField(RealField(105)); n:=(5+3*Sqrt(5))/10; Reverse(Intseq(Floor(10^104*n))); // Arkadiusz Wesolowski, Jan 07 2018
(PARI) (5 + 3*sqrt(5))/10 \\ Michel Marcus, Apr 20 2020
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Klaus Brockhaus, Apr 06 2010
STATUS
approved