Code
using System;
using System.Collections.Generic;
using System.Text;

namespace MyTest.Core
{
    public class MyIdentityConverter
    {
        /**//// <summary>
        /// 用一个长度为11的数组用来存储最后的结果.
        /// </summary>
        /// <param name="sq">当前幂次方</param>
        /// <param name="data"></param>
        /// <returns></returns>
        public string[] ConvertTo62(ulong orgin)
        {
            return ConvertTo62(new string[11], -2, orgin);
        }

        public string[] ConvertTo62(int orgin)
        {
            return ConvertTo62(new string[11], -2, (ulong)orgin);
        }

        public string[] ConvertTo62(uint orgin)
        {
            return ConvertTo62(new string[11], -2, (ulong)orgin);
        }

        public string[] ConvertTo62(long orgin)
        {
            return ConvertTo62(new string[11], -2, (ulong)orgin);
        }

        private string[] ConvertTo62(string[] desCode, int sq, ulong orgin)
        {
           
            if (sq == -1)
                return desCode;//递减时已经计算完低位.

            if (desCode.Length != 11 || orgin < 0)
                throw new Exception("参数无效!");

            if (sq == -2)//使用-2作为初始值. 开始计算.
            {
                Console.WriteLine("初始值origin : " + orgin.ToString());
                for (int i = 1; i < data.Length; i++)
                {
                    if (orgin < data[i])
                    {
                        sq = i ;
                        break;
                    }
                    else if (i == data.Length - 1)
                    {
                        sq = 11;
                        break;
                    }
 
                }
                Console.WriteLine("目标位数 : " + sq.ToString());
            }

            if (sq < 0)
                throw new Exception("出错啦");

            int currnetChar = -1;

            for (int k = 0; k < 62; k++)
            {
                if (orgin < (ulong)k * data[sq -1])
                {
                    currnetChar = k - 1;
                    orgin -= (ulong)(k-1) * data[sq -1];
                    Console.WriteLine("当前计算值 : " + orgin);
                    break;
                }
                else if (k == 61)
                {
                    currnetChar = 61;
                    orgin -= (ulong)61 * data[sq - 1];
                    Console.WriteLine("当前计算值 : " + orgin);
                    break;
                }
            }
            Console.WriteLine("当前位字符索引 : " + currnetChar.ToString());

            desCode[11- sq] = charactor[currnetChar].ToString();
            sq -= 1;
            if (sq > 0)
                return ConvertTo62(desCode, sq, orgin);
            else
                return desCode;
        }

        static readonly ulong[] data = new ulong[] { 1, 62, 3844, 238328, 14776336, 916132832, 56800235584, 3521614606208, 218340105584896, 13537086546263552, 839299365868340224 };
        static readonly char[] charactor = new char[] { '0','1','2','3','4','5','6','7','8','9', 'A','B','C','D','E','F','G','H','I','J','K','L','M','N','O','P','Q','R',
            'S','T','U','V','W','X','Y','Z','a','b','c','d','e','f','g','h','i','j','k','l','m','n','o','p','q','r','s','t','u','v','w','x','y','z' };
    }
}

Code
       [Test]
        public void ConverterTest()
        {
            MyIdentityConverter converter = new MyIdentityConverter();

            string[] descode = converter.ConvertTo62(DateTime.Now.Ticks);
            Console.WriteLine("转换结果 : " + string.Join(string.Empty,descode));

            string[] descode1 = converter.ConvertTo62(int.MaxValue);
            Console.WriteLine("转换结果 : " + string.Join(string.Empty, descode1));

            string[] descode2 = converter.ConvertTo62(uint.MaxValue);
            Console.WriteLine("转换结果 : " + string.Join(string.Empty, descode2));

            string[] descode3 = converter.ConvertTo62(ulong.MaxValue);
            Console.WriteLine("转换结果 : " + string.Join(string.Empty, descode3));

            DateTime dt = new DateTime(2005, 12, 20);//这里使用时间刻度来创建一个唯一的ID.
            string[] descode4 = converter.ConvertTo62(DateTime.Now.Ticks - dt.Ticks);
            Console.WriteLine("转换结果 : " + string.Join(string.Empty, descode4));

            Assert.IsTrue(true);
        }