Lucas

Returns the nth Lucas number.

Syntax

• Lucas(n)

  • n is a non-negative integer

Description

If n is a non-negative integer, then Lucas(n) is the nth Lucas number. The Lucas numbers L(n) are defined recursively by

       ⎧ 2                      if n = 0
L(n) = ⎨ 1                      if n = 1
       ⎩ L(n − 1) + L(n − 2)    otherwise.

Examples

SequenceVector(0, 20) @ Lucas

(2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364, 2207, 3571, 5778, 9349, 15127)

filter(SequenceVector(0, 50) @ Lucas, IsPrime)

(2, 3, 7, 11, 29, 47, 199, 521, 2207, 3571, 9349, 3010349, 54018521, 370248451, 6643838879)

∑(1/Lucas(n), n, 1, 100)

1.96285817321

Lucas(100)/Fibonacci(100)

2.2360679775	(=√5)

See also

• Fibonacci