OFFSET
2,4
COMMENTS
Continued fraction expansion of 5 + sqrt(26) is A010692.
This is the shape of a 10-extension rectangle; see A188640 for definitions. - Clark Kimberling, Apr 09 2011
LINKS
Daniel Starodubtsev, Table of n, a(n) for n = 2..10000
Wikipedia, Metallic mean
FORMULA
a(n) = A010481(n-2) for n > 3.
Equals exp(arcsinh(5)), since arcsinh(x) = log(x + sqrt(x^2 + 1)). - Stanislav Sykora, Nov 01 2013
Equals limit_{n->infinity} S(n, 2*sqrt(2*13))/ S(n-1, 2*sqrt(2*13)), with the S-Chebyshev polynomilas (see A049310). - Wolfdieter Lang, Nov 15 2023
EXAMPLE
5+sqrt(26) = 10.09901951359278483002...
MATHEMATICA
r=10; t = (r + (4+r^2)^(1/2))/2; FullSimplify[t]
N[t, 130]
RealDigits[N[t, 130]][[1]]
RealDigits[5+Sqrt[26], 10, 120][[1]] (* Harvey P. Dale, Jun 24 2013 *)
PROG
(PARI) 5+sqrt(26) \\ Michel Marcus, Jul 23 2018
CROSSREFS
KEYWORD
AUTHOR
Klaus Brockhaus, Apr 24 2010
STATUS
approved