A176458 Decimal expansion of 4+sqrt(17).

8, 1, 2, 3, 1, 0, 5, 6, 2, 5, 6, 1, 7, 6, 6, 0, 5, 4, 9, 8, 2, 1, 4, 0, 9, 8, 5, 5, 9, 7, 4, 0, 7, 7, 0, 2, 5, 1, 4, 7, 1, 9, 9, 2, 2, 5, 3, 7, 3, 6, 2, 0, 4, 3, 4, 3, 9, 8, 6, 3, 3, 5, 7, 3, 0, 9, 4, 9, 5, 4, 3, 4, 6, 3, 3, 7, 6, 2, 1, 5, 9, 3, 5, 8, 7, 8, 6, 3, 6, 5, 0, 8, 1, 0, 6, 8, 4, 2, 9, 6, 6, 8, 4, 5, 4

Offset: 1

Author

Klaus Brockhaus, Apr 20 2010

Keywords

• nonn
• cons
• easy

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

Examples

			4+sqrt(17) = 8.12310562561766054982...
		

Links

• Wikipedia, Metallic mean
• Index entries for algebraic numbers, degree 2

Crossrefs

Cf. A010473 (decimal expansion of sqrt(17)), A010731 (all 8's sequence).

Cf. A049310.

Programs

Mathematica

r=8; t = (r + (4+r^2)^(1/2))/2; FullSimplify[t]
N[t, 130]
RealDigits[N[t, 130]][[1]]

PARI

4+sqrt(17) \\ Charles R Greathouse IV, Jul 24 2013

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