Find difference pattern of the given sequence.

This one is from the interview question I have asked. A sequence was given to me and asked to write a SQL query to find the difference pattern of the sequence and complete the sequence by adding missing numbers.
Give sequence:  '1,5,13,21,25,29,41'
Below is the query to find the answer:

SET NOCOUNT ON

 DECLARE @temp AS TABLE (Id INT IDENTITY, Nums INT, NextNum INT DEFAULT 0,

 Pattern AS (NextNum - Nums)

 )

 INSERT @temp (Nums)

 SELECT * FROM dbo.Split('1,5,13,21,25,29,41', ',')

-- Here assume that Split function you have added already OR please follow the link 
-- http://anishrana.blogspot.in/2012/03/split-string-in-sql-server-using-xml.html
-- and create one.

 UPDATE a

       SET NextNum = b.Nums

 FROM @temp a

 JOIN @temp b ON a.Id = (b.Id - 1)

 DECLARE @pattern INT = NULL,

              @firstNum INT = NULL,

              @lastNum INT = NULL

 SELECT TOP 1 @pattern = Pattern FROM @temp a

 GROUP BY Pattern

 ORDER BY COUNT(1) DESC

 SELECT @firstNum = MIN(Nums), @lastNum = MAX(Nums) FROM @temp

 --SELECT @pattern, @firstNum, @lastNum

WHILE (@lastNum >= @firstNum)

BEGIN

       PRINT @firstNum

       SET @firstNum += @pattern

END

PRINT 'Sequence generated with difference pattern of: ' + CONVERT(NVARCHAR(10), @pattern)

SET NOCOUNT OFF

Copy and run the script in SQL.

Below is the result:
--------------------------------------------------------------------

1

5

9

13

17

21

25

29

33

37

41

Sequence generated with difference pattern of: 4