MySQL 8.0

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CREATE TABLE `test_nested_order_by` (
  `id` int(11) NOT NULL,
  `timestamp` int(11) NOT NULL COMMENT 'Timestamp',
  `index_continuity_month` int(11) NOT NULL
) ENGINE=MyISAM DEFAULT CHARSET=utf8;

insert into test_nested_order_by (id,timestamp,index_continuity_month) values (1,1583772141,0) ;
insert into test_nested_order_by (id,timestamp,index_continuity_month) values (1,1583708400,0) ;
insert into test_nested_order_by (id,timestamp,index_continuity_month) values (5,1583708400,0) ;
insert into test_nested_order_by (id,timestamp,index_continuity_month) values (4,1583708400,0) ;
insert into test_nested_order_by (id,timestamp,index_continuity_month) values (5,1583794800,0) ;
insert into test_nested_order_by (id,timestamp,index_continuity_month) values (4,1583794800,0) ;
select * from test_nested_order_by order by id, timestamp


id
timestamp
index_continuity_month


1
1583708400
0

1
1583772141
0

4
1583708400
0

4
1583794800
0

5
1583708400
0

5
1583794800
0


update test_nested_order_by t
inner join (
	select 
		t.*, 
		row_number() over(order by id, timestamp) rn 
	from test_nested_order_by t
) t1 on t1.id = t.id and t1.timestamp = t.timestamp
set t.index_continuity_month  = t1.rn 
select * from test_nested_order_by order by id, timestamp


id
timestamp
index_continuity_month


1
1583708400
1

1
1583772141
2

4
1583708400
3

4
1583794800
4

5
1583708400
5

5
1583794800
6


update test_nested_order_by set index_continuity_month = 0
update test_nested_order_by t
inner join (
	select t.*, @rn := @rn + 1 rn
	from (select * from test_nested_order_by order by id, timestamp) t
	cross join (select @rn := 0) x
) t1 on t1.id = t.id and t1.timestamp = t.timestamp
set t.index_continuity_month  = t1.rn 
select * from test_nested_order_by order by id, timestamp


id
timestamp
index_continuity_month


1
1583708400
1

1
1583772141
2

4
1583708400
3

4
1583794800
4

5
1583708400
5

5
1583794800
6
id	timestamp	index_continuity_month
1	1583708400	0
1	1583772141	0
4	1583708400	0
4	1583794800	0
5	1583708400	0
5	1583794800	0