A100727 Continued fraction expansion of (1/2) [tan(1) + sec(1)].

1, 1, 2, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 5, 1, 2, 1, 6, 1, 2, 1, 7, 1, 2, 1, 8, 1, 2, 1, 9, 1, 2, 1, 10, 1, 2, 1, 11, 1, 2, 1, 12, 1, 2, 1, 13, 1, 2, 1, 14, 1, 2, 1, 15, 1, 2, 1, 16, 1, 2, 1, 17, 1, 2, 1, 18, 1, 2, 1, 19, 1, 2, 1, 20, 1, 2, 1, 21, 1, 2, 1, 22, 1, 2, 1, 23, 1

Offset: 0

Author

Ralf Stephan, Nov 24 2004

Keywords

• nonn
• cofr
• easy

Comments

Periodic part is ...1,2,1,k,..., for k=2..oo.

Examples

			1.704111721167913924209364024428505183278823713737764668609552441...
		

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,0,2,0,0,0,-1).

Crossrefs

Cf. A093178, A100261.

Programs

Mathematica

ContinuedFraction[(Tan[1]+Sec[1])/2,100] (* Harvey P. Dale, Feb 11 2015 *)

Formula

G.f.: (x^4-x^2-1)*(x^6+x^5+x^4-x^3-x^2-x-1) / ((x-1)^2*(x+1)^2*(x^2+1)^2). - Colin Barker, Jul 16 2013