DECLARE @BegYr INT = 2013, @EndYr INT = 2015
DECLARE @CombYr VARCHAR(10) = ''

;WITH Tally AS (SELECT n = 0 UNION ALL SELECT 1 UNION ALL SELECT 2 UNION ALL SELECT 3 UNION ALL SELECT 4)

SELECT @CombYr = @CombYr + '/'+RIGHT(@BegYr + n,1) 
FROM Tally
WHERE @BegYr + n BETWEEN @BegYr AND @EndYr

SELECT STUFF(@CombYr,1,1,'')

   DECLARE @BegYr INT = 2013
   DECLARE @EndYr INT = 2015
   DECLARE @E INT
   DECLARE @A VARCHAR(10)
   DECLARE @Z VARCHAR(10)
   SET @E = @BegYr
   SET @Z = (SELECT SUBSTRING(CAST(@E AS VARCHAR(4)),LEN(CAST(@E AS VARCHAR(4))),LEN(CAST(@E AS VARCHAR(4)))))
	  WHILE @E < @EndYr
        BEGIN
	     SET @E = @E + 1
         SET @A = (SELECT '/' + SUBSTRING(CAST(@E AS VARCHAR(4)),LEN(CAST(@E AS VARCHAR(4))),LEN(CAST(@E AS VARCHAR(4)))))
		 SET @Z = @Z + @A
		 
	    END
   SELECT @Z 

Result:

3/4/5

   DECLARE @BegYr INT = 2013
   DECLARE @EndYr INT = 2015
   DECLARE @E INT
   DECLARE @A VARCHAR(10)
   DECLARE @Z VARCHAR(10)
   SET @E = @BegYr
   SET @Z = (SELECT SUBSTRING(CAST(@E AS VARCHAR(4)),LEN(CAST(@E AS VARCHAR(4))),LEN(CAST(@E AS VARCHAR(4)))))
	  WHILE @E < @EndYr
        BEGIN
	     SET @E = @E + 1
         SET @A = (SELECT '/' + SUBSTRING(CAST(@E AS VARCHAR(4)),LEN(CAST(@E AS VARCHAR(4))),LEN(CAST(@E AS VARCHAR(4)))))
		 SET @Z = @Z + @A
		 
	    END
   SELECT @Z 

Result:

3/4/5

DECLARE @BegYr INT = 2013,
        @EndYr INT = 2015,
        @OddReq VARCHAR(32);

WITH quickTally(n) AS (SELECT TOP(@EndYr - @BegYr + 1) n FROM (VALUES (0),(1),(2),(3),(4),(5),(6),(7),(8),(9),(10))dt(n))
select
    @OddReq = stuff((select '/' + right(cast(@BegYr + n as varchar),1)
                     from quickTally
                     for xml path(''),type).value('.','varchar(32)'),1,1,'');

select @OddReq;
go

--goal: Output CombYr = 3/4/5
--Input: BegYr int, EndYr int
--assume inputs are valid. and year is 4-digit format. and EndYr - BegYr <= 10

DECLARE @BegYr INT = 2010, @EndYr INT = 2020;
DECLARE @YrDiff SMALLINT, @CurrentYr SMALLINT,  @CombYr VARCHAR(250)= '';

SET @YrDiff = @EndYr - @BegYr; --difference btw start and end year
SET @CurrentYr = CAST(SUBSTRING(CAST(@BegYr AS CHAR(4)),4,1) AS SMALLINT); --last digit of current year
WHILE @YrDiff >= 0 
BEGIN
	IF @YrDiff = 0
		SET @CombYr = @CombYr + CAST(@CurrentYr AS VARCHAR(3));
	ELSE
		SET @CombYr = @CombYr + CAST(@CurrentYr AS VARCHAR(3))+ '/';
	
	SET @YrDiff = @YrDiff - 1;
	SET @CurrentYr = @CurrentYr + 1;
END 
	
SELECT @CombYr AS CombinedYearOuput; --output result

IF OBJECT_ID('tempdb..#Years') IS NOT NULL
DROP TABLE #Years

IF OBJECT_ID('tempdb..#Results') IS NOT NULL
DROP TABLE #Results

--a table to hold the sample data
CREATE TABLE #Years (
    [ID] INT IDENTITY(1,1) NOT NULL,
    [StartYear] DATE NULL,
    [EndYear] DATE NULL,
    PRIMARY KEY (ID))
    
DECLARE
     @RandomStartDate DATE
    ,@RandomEndDate DATE
    ,@Counter INT
    ,@NumSampleRows INT

SET @Counter = 1    
SET @NumSampleRows = 10    --change this to as many sample as you want
    
--populate the sample table with random dates
WHILE @Counter < = @NumSampleRows
    BEGIN
        SET @RandomStartDate = DATEADD(day,(ABS(CHECKSUM(NEWID()))%65530),0)
        SET @RandomEndDate = DATEADD(year,(ABS(CAST(NEWID() AS BINARY(6))%10)+1),@RandomStartDate)
        INSERT INTO #Years VALUES (@RandomStartDate,@RandomEndDate)
        SET @Counter = @Counter + 1
    END

--a table for the results
CREATE TABLE #Results (
    [ID] INT NOT NULL,
    [StartYear] DATE NULL,
    [EndYear] DATE NULL,
    [DYears] VARCHAR(255) NULL,
    PRIMARY KEY (ID))
    

DECLARE 
     @x INT
    ,@NumRows INT
    
SET @x = 1
SET @NumRows = (SELECT MAX(ID) FROM #Years)

--create the string of single digit years for each row in the table
WHILE @x <= @NumRows
    BEGIN

        INSERT INTO #Results
        SELECT
            ID
           ,StartYear
           ,EndYear
           ,(SELECT
                STUFF(CAST(t1.N AS CHAR(4)),1,3,'')+'/'
            FROM
                (
                SELECT
                     ID
                    ,CAST(YEAR(y.StartYear) AS CHAR(4)) AS SYear
                    ,CAST(YEAR(y.EndYear) AS CHAR(4))AS EYear    
                FROM
                    #Years AS y    
                ) r
            LEFT OUTER JOIN
                dbo.Tally AS t1
                ON t1.N > 0
            WHERE
                t1.N BETWEEN SYear AND EYear
                AND r.ID = @x
            FOR XML PATH('')
            ) AS DYears
        FROM
            #Years
        WHERE
            ID = @x
        
        
        SET @x = @x + 1

    END

SELECT * FROM #Results

ID	StartYear	EndYear		DYears
1	1919-03-28	1927-03-28	9/0/1/2/3/4/5/6/7/
2	2028-07-26	2030-07-26	8/9/0/
3	1977-04-11	1983-04-11	7/8/9/0/1/2/3/
4	1966-05-04	1967-05-04	6/7/
5	2018-03-27	2019-03-27	8/9/
6	2024-03-28	2026-03-28	4/5/6/
7	1966-02-23	1975-02-23	6/7/8/9/0/1/2/3/4/5/
8	1988-08-21	1996-08-21	8/9/0/1/2/3/4/5/6/
9	2061-02-02	2063-02-02	1/2/3/
10	1974-11-01	1981-11-01	4/5/6/7/8/9/0/1/

IF OBJECT_ID('tempdb..#Years') IS NOT NULL
DROP TABLE #Years

--a table to hold the sample data
CREATE TABLE #Years (
    [ID] INT IDENTITY(1,1) NOT NULL,
    [StartYear] DATE NULL,
    [EndYear] DATE NULL,
    PRIMARY KEY (ID))
    
DECLARE @NumSampleRows INT 
SET @NumSampleRows = 10

;WITH Tally (n) AS (
    SELECT TOP (@NumSampleRows) ROW_NUMBER() OVER (ORDER BY (SELECT NULL))
    FROM sys.all_columns)
INSERT INTO #Years
SELECT [StartYear]
    ,[EndYear]=DATEADD(day, ABS(CHECKSUM(NEWID())) % 6000, [StartYear])
FROM Tally
CROSS APPLY (SELECT [StartYear]=DATEADD(day, ABS(CHECKSUM(NEWID())) % 50000, 0)) a

SELECT ID, [StartYear], [EndYear], OddStr=(
    SELECT CASE n WHEN 0 THEN '' ELSE '/' END + 
        CAST(YEAR(DATEADD(year, n, StartYear))%10 AS VARCHAR)
    FROM (
        SELECT 0 UNION ALL SELECT TOP (DATEDIFF(year, [StartYear], [EndYear]))
            ROW_NUMBER() OVER (ORDER BY (SELECT NULL))
        FROM sys.all_columns) a(n)
    ORDER BY n
    FOR XML PATH('')) 
FROM #Years
GROUP BY ID, [StartYear], [EndYear]

IF OBJECT_ID('tempdb..#Years') IS NOT NULL
DROP TABLE #Years