Might not be the most efficient way but seems to meet your criteria, no?

CREATE TABLE #TmpTbl (RowId INT IDENTITY(1,1), ACTCODE NCHAR(6));

INSERT INTO #TmpTbl (ACTCODE) VALUES ('110001'), ('110003'), ('110009'), ('120000'), ('120001');

DECLARE @SEQUENCE NCHAR(6) = 220000;

SELECT * FROM #TmpTbl;

UPDATEtmp

SETACTCODE = s.sACTCODE

FROM#TmpTbl tmp

INNER JOIN (

SELECTACTCODE

, sACTCODE = @SEQUENCE + ROW_NUMBER() OVER (ORDER BY ACTCODE)

FROM#TmpTbl

WHEREACTCODE BETWEEN 110001 AND 110009

) s ON tmp.ACTCODE = s.ACTCODE;

SELECT * FROM #TmpTbl;

DROP TABLE #TmpTbl;