This page follows on from an Introduction to the Lucas Numbers. They are a variation on The Fibonacci Numbers. The Lucas numbers are defined very similarly to the Fibonacci numbers, but start with 2 and 1 (in this order) rather than the Fibonacci's 0 and 1:

2024年10月29日 · Lucas numbers are similar to Fibonacci numbers. Lucas numbers are also defined as the sum of its two immediately previous terms. But here the first two terms are 2 and 1 whereas in Fibonacci numbers the first two terms are 0 and 1 respectively.

The Lucas numbers or Lucas series are an integer sequence named after the mathematician François Édouard Anatole Lucas (1842–91), who studied both that sequence and the closely related Fibonacci numbers.

The Lucas numbers are the sequence of integers {L_n}_(n=1)^infty defined by the linear recurrence equation L_n=L_(n-1)+L_(n-2) (1) with L_1=1 and L_2=3. The nth Lucas number is implemented in the Wolfram Language as LucasL[n].

The Lucas numbers or Lucas series, and their fascinating connections with the Fibonacci numbers and the golden section. The first 200 Lucas numbers, and lots of investigations and You do the maths... to find your own formulas and patterns in the series.

1999年5月25日 · The only Square Numbers in the Lucas sequence are 1 and 4, as proved by John H. E. Cohn (Alfred 1964). The only Triangular Lucas numbers are 1, 3, and 5778 (Ming 1991). The only Lucas Cubic Number is 1.

The best-known properties and formulas of the Fibonacci and Lucas numbers. Simple values at zero and infinity. The Fibonacci and Lucas numbers and have the following values at zero and infinity:

A Lucas number is a number which appears in the Lucas sequence or alternatively the index of a number in the series. For example, the 6th Lucas number is 18, and 18 is also a Lucas number since it's in the series.

2017年11月5日 · The sequence of Lucas numbers is named after the mathematician François Édouard Anatole Lucas (1842–1891), who studied both that sequence and the closely related sequence of Fibonacci numbers (both sequences are Lucas sequences).

The Lucas numbers satisfy remarkable difference equations, in some cases best expressed using Fibonacci numbers, of which representative examples are the following: L(n) - L(n - 3) = 2*L(n - 2); L(n) - L(n - 4) = 5*F(n - 2);