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

namespace Algorithms.Sequences
{
    /// <summary>
    ///     <para>
    ///         Sequence of Kummer numbers (also called Euclid numbers of the second kind):
    ///         -1 + product of first n consecutive primes.
    ///     </para>
    ///     <para>
    ///         Wikipedia: https://wikipedia.org/wiki/Euclid_number.
    ///     </para>
    ///     <para>
    ///         OEIS: https://oeis.org/A057588.
    ///     </para>
    /// </summary>
    public class KummerNumbersSequence : ISequence
    {
        /// <summary>
        /// Gets sequence of Kummer numbers.
        /// </summary>
        public IEnumerable<BigInteger> Sequence
        {
            get
            {
                var primorialNumbers = new PrimorialNumbersSequence().Sequence.Skip(1);

                foreach (var n in primorialNumbers)
                {
                    yield return n - 1;
                }
            }
        }
    }
}