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
Famous quotes containing the word definition:
“... we all know the wag’s definition of a philanthropist: a man whose charity increases directly as the square of the distance.”
—George Eliot [Mary Ann (or Marian)
“The very definition of the real becomes: that of which it is possible to give an equivalent reproduction.... The real is not only what can be reproduced, but that which is always already reproduced. The hyperreal.”
—Jean Baudrillard (b. 1929)
“Was man made stupid to see his own stupidity?
Is God by definition indifferent, beyond us all?
Is the eternal truth man’s fighting soul
Wherein the Beast ravens in its own avidity?”
—Richard Eberhart (b. 1904)