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

namespace Algorithms.Sequences
{
    /// <summary>
    ///     <para>
    ///         Sequence of Fermat numbers: a(n) = 2^(2^n) + 1.
    ///     </para>
    ///     <para>
    ///         Wikipedia: https://wikipedia.org/wiki/Fermat_number.
    ///     </para>
    ///     <para>
    ///         OEIS: https://oeis.org/A000215.
    ///     </para>
    /// </summary>
    public class FermatNumbersSequence : ISequence
    {
        /// <summary>
        /// Gets sequence of Fermat numbers.
        /// </summary>
        public IEnumerable<BigInteger> Sequence
        {
            get
            {
                var n = new BigInteger(2);

                while (true)
                {
                    yield return n + 1;
                    n *= n;
                }
            }
        }
    }
}