1,1
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
Table of n, a(n) for n=1..105.
Wikipedia, Metallic mean
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
6.16227766016837933199...
Digits:=100; evalf(3+sqrt(10)); # Wesley Ivan Hurt, Mar 07 2014
r=6; t=(r+(4+r^2)^(1/2))/2; RealDigits[N[t, 130]][[1]] (* Clark Kimberling, Apr 09 2011 *)
(PARI) 3+sqrt(10) \\ Charles R Greathouse IV, Jul 24 2013
Cf. A010467 (decimal expansion of sqrt(10)), A010722 (all 6's sequence).
Sequence in context: A109918 A263494 A096956 * A078300 A318478 A221210
Adjacent sequences: A176395 A176396 A176397 * A176399 A176400 A176401
cons,nonn
Klaus Brockhaus, Apr 16 2010
approved