OFFSET
1,1
COMMENTS
Continued fraction expansion of 3+sqrt(10) is A010722.
This is the shape of a 6-extension rectangle; see A188640 for definitions. - Clark Kimberling, Apr 09 2011
LINKS
Daniel Starodubtsev, Table of n, a(n) for n = 1..10000
Wikipedia, Metallic mean.
FORMULA
a(n) = A010467(n) for n >= 2.
Equals exp(arcsinh(3)), since arcsinh(x) = log(x+sqrt(x^2+1)). - Stanislav Sykora, Nov 01 2013
Equals lim_{n->oo} S(n, 2*sqrt(10))/ S(n-1, 2*sqrt(10)), with the S-Chebyshev polynomials (see A049310). - Wolfdieter Lang, Nov 15 2023
EXAMPLE
6.16227766016837933199...
MAPLE
Digits:=100; evalf(3+sqrt(10)); # Wesley Ivan Hurt, Mar 07 2014
MATHEMATICA
r=6; t=(r+(4+r^2)^(1/2))/2; RealDigits[N[t, 130]][[1]] (* Clark Kimberling, Apr 09 2011 *)
PROG
(PARI) 3+sqrt(10) \\ Charles R Greathouse IV, Jul 24 2013
CROSSREFS
KEYWORD
AUTHOR
Klaus Brockhaus, Apr 16 2010
STATUS
approved