Definition
Similarly to the Fibonacci numbers, each Lucas number is defined to be the sum of its two immediate previous terms, i.e. it is a Fibonacci integer sequence. 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 Lucas numbers may thus be defined as follows:
The sequence of Lucas numbers begins:
- (sequence A000032 in OEIS).
All Fibonacci-like integer sequences appear in shifted form as a row of the Wythoff array; the Fibonacci sequence itself is the first row and the Lucas sequence is the second row. Also like all Fibonacci-like integer sequences, the ratio between two consecutive Lucas numbers converges to the golden ratio.
Read more about this topic: Lucas Number
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