The decomposition of a positive integer into M 2 of N-th square and

-- =============================================

--Author: <maco_wang>

--Create Date: <2011-01-21>

--Description: < decomposition of a positive integer into M 2 of N-th square and >

-- =============================================

Go

--Create a function

CREATE function getsumsequence (@num INT)

Returns nvarchar (200)

As

BEGIN

DECLARE @numc INT

SET @numc = @num

DECLARE @numstr VARCHAR (50)

SET @numstr = ' '

while (@num <> 0)

BEGIN

SET @numstr = @numstr + CONVERT (CHAR (1), @num% 2)

SET @num = @num/2

END

--select REVERSE (@numstr)

DECLARE @i INT

SET @i = LEN (@numstr)

DECLARE @j VARCHAR (MAX)

SET @j = "

while (@i > 0)

BEGIN

IF (SUBSTRING (REVERSE (@numstr), LEN (@numstr)-@i + 1, 1) = ' 1 ')

SELECT @j = @j + ' +2^ ' + CAST (@i-1 as VARCHAR (10))

SET @i = @i-1

END

Return (CAST (@numc as VARCHAR) + ' = ' + STUFF (@j, 1, 1, '))

END

Go

--Test example

SELECT dbo. Getsumsequence (12)

SELECT dbo. Getsumsequence (65)

SELECT dbo. Getsumsequence (892)

SELECT dbo. Getsumsequence (1919191)

--Running results

/*

12=2^3+2^2

65=2^6+2^0

892=2^9+2^8+2^6+2^5+2^4+2^3+2^2

1919191=2^20+2^19+2^18+2^16+2^14+2^11+2^7+2^6+2^4+2^2+2^1+2^0

*/

The decomposition of a positive integer into M 2 of N-th square and