The Lucas numbers are a Fibonacci-style sequence with seed values \(L_0 = 2\), \(L_1 = 1\). Each subsequent term is the sum of the two preceding: 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199.
Lucas and Fibonacci numbers are deeply intertwined: \(L_n = F_{n-1} + F_{n+1}\), and \(L_n^2 - 5 F_n^2 = 4(-1)^n\). Like Fibonacci, the ratio of consecutive Lucas numbers converges to the golden ratio \(\varphi\).
Named after the 19th-century French mathematician Édouard Lucas, who used these sequences in his work on primality testing — the Lucas–Lehmer test is still the standard way to certify Mersenne primes.