OFFSET
1,1
COMMENTS
Continued fraction expansion of 4+sqrt(17) is A010731.
This is the shape of an 8-extension rectangle; see A188640 for definitions. - Clark Kimberling, Apr 09 2011
LINKS
FORMULA
a(n) = A010473(n) for n > 1.
Equals exp(arcsinh(4)), since arcsinh(x)=log(x+sqrt(x^2+1)). - Stanislav Sykora, Nov 01 2013
Equals lim_{n->infinity} S(n, 2*sqrt(17))/S(n-1, 2*sqrt(17)), with the S-Chebyshev polynomials (see A049310). - Wolfdieter Lang, Nov 15 2023
EXAMPLE
4+sqrt(17) = 8.12310562561766054982...
MATHEMATICA
r=8; t = (r + (4+r^2)^(1/2))/2; FullSimplify[t]
N[t, 130]
RealDigits[N[t, 130]][[1]]
PROG
(PARI) 4+sqrt(17) \\ Charles R Greathouse IV, Jul 24 2013
CROSSREFS
KEYWORD
AUTHOR
Klaus Brockhaus, Apr 20 2010
STATUS
approved