Maths - Lucas Series Generator

Introduction:

This page allows you to generate the elements of the 'Lucas Series' - a close relative of the classic Fibonacci series.
One outstanding feature of both series, is that the difference between each result and the next, gets infinitely close to "The Golden Ratio", often denoted by the Greek Letter Phi: φ
You may choose between a numbered list, or an unformatted sequence of results. Both will have exactly the same entries. Please note that beyond about 200 values, the numbers displayed will start to get too long to display on a single line. The 'numbered list' result style is therefore formatted to allow the lines to wrap; the 'simple list' style displays unformatted numbers that can more easily be used in other software.

Formulae:

The Lucas sequence can be defined as: n[x] = n[x-1] + n[x-2] (just like the Fibonacci sequence), but:
Where: n[1] = 1 and n[2] = 3   (unlike 1 & 1 for Fibonacci)
and: x is the current element number, or 'index'

Instructions

If you change the 'Number of entries to generate' box, after a list has been generated, the original list will be expanded from where it previously finished.
If you have a very old computer, and choose to calculate a long list, the system may become temporarily unresponsive. If this proves problematic, choose a small number first, then increase gradually. Only new values will be created each time.
Settings

Results:


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