using System.Collections.Generic;
using System.Numerics;

namespace Algorithms.Sequences
{
    /// <summary>
    ///     <para>
    ///         Sequence of Lucas number values.
    ///     </para>
    ///     <para>
    ///         Wikipedia: https://en.wikipedia.org/wiki/Lucas_number.
    ///     </para>
    ///     <para>
    ///         OEIS: http://oeis.org/A000032.
    ///     </para>
    /// </summary>
    public class LucasNumbersBeginningAt2Sequence : ISequence
    {
        /// <summary>
        ///     <para>
        ///         Gets Lucas number sequence.
        ///     </para>
        ///     <para>
        ///         Lucas numbers follow the same type of operation that the Fibonacci (A000045)
        ///         sequence performs with starting values of 2, 1 versus 0,1.  As Fibonacci does,
        ///         the ratio between two consecutive Lucas numbers converges to phi.
        ///     </para>
        ///     <para>
        ///         This implementation is similar to A000204, but starts with the index of 0, thus having the
        ///         initial values being (2,1) instead of starting at index 1 with initial values of (1,3).
        ///     </para>
        ///     <para>
        ///         A simple relationship to Fibonacci can be shown with L(n) = F(n-1) + F(n+1), n>= 1.
        ///
        ///         n |  L(n) | F(n-1) | F(n+1)
        ///         --|-------|--------+--------+
        ///         0 |   2   |        |        |
        ///         1 |   1   |      0 |      1 |
        ///         2 |   3   |      1 |      2 |
        ///         3 |   4   |      1 |      3 |
        ///         4 |   7   |      2 |      5 |
        ///         5 |  11   |      3 |      8 |
        ///         --|-------|--------+--------+.
        ///     </para>
        /// </summary>
        public IEnumerable<BigInteger> Sequence
        {
            get
            {
                yield return 2;
                yield return 1;
                BigInteger previous = 2;
                BigInteger current = 1;
                while (true)
                {
                    var next = previous + current;
                    previous = current;
                    current = next;

                    yield return next;
                }
            }
        }
    }
}