Logical reads for seeks on a non unique clustered index - sql-server

Question

For the table definition
CREATE TABLE Accounts
(
AccountID INT ,
Filler CHAR(1000)
)
Containing 21 rows (7 for each of the AccountId values 4,6,7).
It has 1 root page and 4 leaf pages
index_depth page_count index_level
----------- -------------------- -----------
2 4 0
2 1 1
The root page looks like
FileId PageId ROW LEVEL ChildFieldId ChildPageId AccountId (KEY) UNIQUIFIER (KEY) KeyHashValue
----------- ----------- ----------- ----------- ------------ ----------- --------------- ---------------- ------------------------------
1 121 0 1 1 119 NULL NULL NULL
1 121 1 1 1 151 6 0 NULL
1 121 2 1 1 175 6 3 NULL
1 121 3 1 1 215 7 1 NULL
The actual distribution of AccountId records over these pages is
AccountID page_id Num
----------- ----------- -----------
4 119 7
6 151 3
6 175 4
7 175 1
7 215 6
The Query
SELECT AccountID
FROM Accounts
WHERE AccountID IN (4,6,7)
Gives the following IO stats
Table 'Accounts'. Scan count 3, logical reads 13
Why?
I thought for each seek it would seek into the first page that might potentially contain that value and then (if necessary) continue along the linked list until it found the first row not equal to the seeked value.
However that only adds up to 10 page accesses
4) Root Page -> Page 119 -> Page 151 (Page 151 Contains a 6 so should stop)
6) Root Page -> Page 119 -> Page 151 -> Page 175 (Page 175 Contains a 7 so should stop)
7) Root Page -> Page 175 -> Page 215 (No more pages)
So what accounts for the additional 3?
Full script to reproduce
USE tempdb
SET NOCOUNT ON;
CREATE TABLE Accounts
(
AccountID INT ,
Filler CHAR(1000)
)
CREATE CLUSTERED INDEX ix ON Accounts(AccountID)
INSERT INTO Accounts(AccountID)
SELECT C
FROM (SELECT 4 UNION ALL SELECT 6 UNION ALL SELECT 7) Vals(C)
CROSS JOIN (SELECT TOP (7) 1 FROM master..spt_values) T(X)
DECLARE #AccountID INT
SET STATISTICS IO ON
SELECT #AccountID=AccountID FROM Accounts WHERE AccountID IN (4,6,7)
SET STATISTICS IO OFF
SELECT index_depth,page_count,index_level
FROM
sys.dm_db_index_physical_stats (2,OBJECT_ID('Accounts'), DEFAULT,DEFAULT, 'DETAILED')
SELECT AccountID, P.page_id, COUNT(*) AS Num
FROM Accounts
CROSS APPLY sys.fn_PhysLocCracker(%%physloc%%) P
GROUP BY AccountID, P.page_id
ORDER BY AccountID, P.page_id
DECLARE #index_info TABLE
(PageFID VARCHAR(10),
PagePID VARCHAR(10),
IAMFID TINYINT,
IAMPID INT,
ObjectID INT,
IndexID TINYINT,
PartitionNumber TINYINT,
PartitionID BIGINT,
iam_chain_type VARCHAR(30),
PageType TINYINT,
IndexLevel TINYINT,
NextPageFID TINYINT,
NextPagePID INT,
PrevPageFID TINYINT,
PrevPagePID INT,
PRIMARY KEY (PageFID, PagePID));
INSERT INTO #index_info
EXEC ('DBCC IND ( tempdb, Accounts, -1)' );
DECLARE #DynSQL NVARCHAR(MAX) = 'DBCC TRACEON (3604);'
SELECT #DynSQL = #DynSQL + '
DBCC PAGE(tempdb, ' + PageFID + ', ' + PagePID + ', 3); '
FROM #index_info
WHERE IndexLevel = 1
SET #DynSQL = #DynSQL + '
DBCC TRACEOFF(3604); '
CREATE TABLE #index_l1_info
(FileId INT,
PageId INT,
ROW INT,
LEVEL INT,
ChildFieldId INT,
ChildPageId INT,
[AccountId (KEY)] INT,
[UNIQUIFIER (KEY)] INT,
KeyHashValue VARCHAR(30));
INSERT INTO #index_l1_info
EXEC(#DynSQL)
SELECT *
FROM #index_l1_info
DROP TABLE #index_l1_info
DROP TABLE Accounts

Answer 1

Just to supply the answer in answer form rather than as discussion in the comments...
The additional reads arise due to the read ahead mechanism. This scans the parent pages of the leaf level in case it needs to issue an asynchronous IO to bring the leaf level pages into the buffer cache so they are ready when the range seek reaches them.
It is possible to use trace flag 652 to disable the mechanism (server wide) and verify that the number of reads is now exactly 10 as expected.

Answer 2

From what I see from the output of DBCC IND, there is 1 root page (type = 10), 1 key page (type = 2) and four leaf pages (type = 1), total of 6 pages.
So each scan goes as root -> key -> leaf -> … -> final leaf which gives 4 reads for 4 and 7 and 5 reads for 6, total 4 + 4 + 5 = 13.