Find user having continuously three year of attendenance

with events as(
--setup dummy data
	select 
		1 id,
		'Arun' name,
		2001 year
	union all select 2, 'Arun', 2002
	union all select 3, 'Arun', 2003
	union all select 4, 'Arun', 2004
	union all select 5, 'Arun', 2009
	union all select 6, 'Arun', 2010
	union all select 7, 'Arun', 2011
	union all select 8, 'Bala', 2014
	union all select 9, 'Bala', 2015
	union all select 10, 'Bala', 2017
	union all select 11, 'chan', 2014
	union all select 12, 'chan', 2015
	union all select 13, 'chan', 2018
--extra data
	union all select 14, 'Arun', 2006
	union all select 15, 'Arun', 2005
	union all select 16, 'Bala', 2018
	union all select 17, 'Bala', 2020
	union all select 18, 'Bala', 2019
	union all select 22, 'Jim', 2009
	union all select 21, 'Jim', 2010
	union all select 20, 'Jim', 2011

), eventsGroup as (
	--part of your sql
	select
		e.*, 
		(year - row_number() over (partition by name order by year)) as grp 
	from events e
), eventsGroup3Year as (
	--do a modulus check
	select
		*, 
		(row_number() over (partition by name, grp order by year))%3 as rowid3
	from eventsGroup
)
select 
	row_number() over(order by  name, year) id,
	name,
	convert(char(4), year-2)+' - '+convert(char(4), year) years
from eventsGroup3Year
where rowid3 = 0
order by
	name,
	year
;

with (
--	...cte as above, up to eventsGroup3Year...
)
, LagYear as(
select 
	*,
	lag(year, 1, 0) over (order by name, year) StartYear
from eventsGroup3Year
where rowid3 = 0 or rowid3 = 1
)
select
	row_number() over(order by name, year) id,
	name,
	concat(StartYear, ' - ', year) Years -- concat via solution 3, thanks Maciej Los
from LagYear where rowid3 = 0
;

DECLARE @tmp TABLE(ID INT, [Name] VARCHAR(30), [Year] INT)

INSERT INTO @tmp (ID, [Name], [Year])
VALUES(1, 'Arun', 2001),
(2, 'Arun', 2002),
(3, 'Arun', 2003),
(4, 'Arun', 2004),
(5, 'Arun', 2009),
(6, 'Arun', 2010),
(7, 'Arun', 2011),
(8, 'Bala', 2014),
(9, 'Bala', 2015),
(10, 'Bala', 2017),
(11, 'chan', 2014),
(12, 'chan', 2015),
(13, 'chan', 2018),
(14, 'zen', 2014),
(15, 'zen', 2015)

--4
SELECT [Name], CONCAT([1], ' - ', [3]) AS Years
FROM (
	--3
	SELECT [Name], [Grp], [1], [2], [3]
	FROM (
		--2
		SELECT [Name], [Year], Grp, ROW_NUMBER() OVER(PARTITION BY [Name], [Grp] ORDER BY [Year]) AS RowNo
		FROM (
			--1
			SELECT [Name], [Year], [Year] - ROW_NUMBER() OVER(PARTITION BY [Name] ORDER BY [Year]) AS Grp
			FROM @tmp
		) AS T
	) AS SRC
	PIVOT(MAX([Year]) FOR [RowNo] IN ([1], [2], [3])) AS PVT
	WHERE COALESCE([3],0) - COALESCE([1],0) = 2
) AS DST

with seq as(
SELECT name, year st
,lead(year) over ( partition by name order by year) nd
,lead(year,2) over ( partition by name order by year) ed
FROM my_tasks.participants
order by name,year)
select name
from seq
where nd is not null
and ed is not null
and ed=nd+1
and nd=st+1
group by name ;