A176537 Decimal expansion of 5 + sqrt(26).

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

Offset: 2

Author

Klaus Brockhaus, Apr 24 2010

Keywords

• cons
• nonn
• easy

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

Examples

			5+sqrt(26) = 10.09901951359278483002...
		

Links

• Daniel Starodubtsev, Table of n, a(n) for n = 2..10000
• Wikipedia, Metallic mean
• Index entries for algebraic numbers, degree 2.

Crossrefs

Cf. A010481 (decimal expansion of sqrt(26)), A010692 (all 10's sequence).

Programs

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 *)

PARI

5+sqrt(26) \\ Michel Marcus, Jul 23 2018

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