The Lucas numbers are an integer sequence named after the mathematician François Édouard Anatole Lucas (1842–1891), who studied both that sequence and the closely related Fibonacci numbers (both are Lucas sequences). Like the Fibonacci numbers, each Lucas number is defined to be the sum of its two immediate previous terms. Consequently, the ratio between two consecutive Lucas numbers converges to the golden ratio.

However, the first two Lucas numbers are L0 = 2 and L1 = 1 instead of 0 and 1, and the properties of Lucas numbers are therefore somewhat different from those of Fibonacci numbers.

sionnach commented on the word lucas numbers

The Lucas numbers are an integer sequence named after the mathematician François Édouard Anatole Lucas (1842–1891), who studied both that sequence and the closely related Fibonacci numbers (both are Lucas sequences). Like the Fibonacci numbers, each Lucas number is defined to be the sum of its two immediate previous terms. Consequently, the ratio between two consecutive Lucas numbers converges to the golden ratio.

However, the first two Lucas numbers are L0 = 2 and L1 = 1 instead of 0 and 1, and the properties of Lucas numbers are therefore somewhat different from those of Fibonacci numbers.

The sequence of Lucas numbers begins:

2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, ..

November 19, 2007