A176055 Decimal expansion of (2+sqrt(5))/2.

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

Offset: 1

Author

Klaus Brockhaus, Apr 07 2010

Keywords

• cons
• easy
• nonn

Comments

Continued fraction expansion of (2+sqrt(5))/2 is A010698.

a(n) = A020837(n-1) for n > 1; a(1) = 2.

Examples

			2.11803398874989484820...
		

Links

• Index entries for algebraic numbers, degree 2.

Crossrefs

Cf. A002163 (sqrt(5)), A020837 (1/sqrt(80)), A010698 (repeat 2, 8).

Cf. A000045, A001622.

Programs

Mathematica

RealDigits[GoldenRatio + 1/2, 10, 100][[1]] (* Amiram Eldar, Jun 06 2021 *)

Formula

Equals 1/2 + phi, with phi = A001622.

From Amiram Eldar, Jun 06 2021: (Start)

Equals 1 + Sum{k>=0} 1/(Fibonacci(2*k+1)+1).

Equals 1 + Sum{k>=0} binomial(2*k,k)/20^k. (End)