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

1,1

Comments

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

Rajan et al. (2010) claim the variance of a discrete distribution generated by the linear convolution of Fibonacci sequence with itself, saturates to a constant of value 8.4721359. - Jonathan Vos Post, May 10 2010

Links

Table of n, a(n) for n=1..105.

Arulalan Rajan, Jamadagni, Vittal Rao, and Ashok Rao, Convolutions Induced Discrete Probability Distributions and a New Fibonacci Constant, arXiv:1005.1231 [math.PR], 2010.

Index entries for algebraic numbers, degree 2.

Formula

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

Minimal polynomial: x^2 - 8*x - 4. - Amiram Eldar, May 04 2026

Example

8.47213595499957939281834733746255247088123671922305...

Mathematica

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

Crossrefs

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

Sequence in context: A388821 A096427 A380982 * A388905 A257775 A242023

Adjacent sequences: A176450 A176451 A176452 * A176454 A176455 A176456

Keyword

cons,nonn

Author

Klaus Brockhaus, Apr 20 2010

Status

approved