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

namespace Algorithms.Sequences
{
    /// <summary>
    ///     <para>
    ///         Sequence of Fermat primes: primes of the form 2^(2^k) + 1, for some k >= 0.
    ///     </para>
    ///     <para>
    ///         Wikipedia: https://wikipedia.org/wiki/Fermat_number.
    ///     </para>
    ///     <para>
    ///         OEIS: https://oeis.org/A019434.
    ///     </para>
    /// </summary>
    public class FermatPrimesSequence : ISequence
    {
        /// <summary>
        /// Gets sequence of Fermat primes.
        /// </summary>
        public IEnumerable<BigInteger> Sequence
        {
            get
            {
                var fermatNumbers = new FermatNumbersSequence().Sequence.Take(5);

                foreach (var n in fermatNumbers)
                {
                    yield return n;
                }
            }
        }
    }
}