VanEcksSequence.cs

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

namespace Algorithms.Sequences
{
    /// <summary>
    ///     <para>
    ///         Van Eck's sequence. For n >= 1, if there exists an m &lt; n such that a(m) = a(n), take the largest such m and set a(n+1) = n-m; otherwise a(n+1) = 0. Start with a(1)=0.
    ///     </para>
    ///     <para>
    ///         OEIS: http://oeis.org/A181391.
    ///     </para>
    /// </summary>
    public class VanEcksSequence : ISequence
    {
        /// <summary>
        ///     Gets Van Eck's sequence.
        /// </summary>
        public IEnumerable<BigInteger> Sequence
        {
            get
            {
                yield return 0;
                var dictionary = new Dictionary<BigInteger, BigInteger>();
                BigInteger previous = 0;
                BigInteger currentIndex = 2; // 1-based index
                while (true)
                {
                    BigInteger element = 0;
                    if (dictionary.TryGetValue(previous, out var previousIndex))
                    {
                        element = currentIndex - previousIndex;
                    }

                    yield return element;

                    dictionary[previous] = currentIndex;
                    previous = element;
                    currentIndex++;
                }
            }
        }
    }
}