A176453 Decimal expansion of 4+2*sqrt(5).

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

Offset: 1

Author

Klaus Brockhaus, Apr 20 2010

Keywords

• cons
• nonn

Comments

Continued fraction expansion of 4+2*sqrt(5) is A010698 preceded by 8.

a(n) = A010476(n) = A020762(n-1) = A134974(n) for n > 1.

Rajan (2010) claims the variance of a discrete distribution generated by the linear convolution of Fibonacci sequence with itself, saturates to a constant of value 8.4721359. [From Jonathan Vos Post, May 10 2010]

Examples

			4+2*sqrt(5) = 8.47213595499957939281...
		

Links

• Arulalan Rajan, Jamadagni, Vittal Rao, Ashok Rao, Convolutions Induced Discrete Probability Distributions and a New Fibonacci Constant, May 6, 2010. [From _Jonathan Vos Post_, May 10 2010]

Crossrefs

Cf. A002163 (decimal expansion of sqrt(5)), A010476 (decimal expansion of sqrt(20)), A020762 (decimal expansion of 1/sqrt(5)), A134974 (decimal expansion of 8/(1+sqrt(5))), A010698 (repeat 2, 8).

Programs

Mathematica

RealDigits[4+2Sqrt[5],10,120][[1]] (* Harvey P. Dale, Sep 08 2018 *)