png to grayscale conversion offset by 1 in pixel intensity

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hi
I am running opencv in ubuntu 14.04
Here I am reading a png file and displaying it , printing value of b,g,r channel at pixel and converting to gray scale (file not changed on disk only in memory).
My code in C

/* usage: prog image assuming filename is  image-1.png*/
#include"cv.h"
#include"highgui.h"
#include"imgproc.hpp"
using namespace cv;

int main( int argc, char** argv )
{   char strimgfile[100];
    int i,j,cn,filenumber=1;
    Mat image;
    Mat gray_image;
    Vec3b intensity;
    unsigned int b,g,r;

    sprintf(strimgfile,"%s%d.png",argv[1],filenumber);//adding number and png extension to program argument which is filename prefix
    printf("\nthe file that will be read _%s_\n",strimgfile);
    image = imread( strimgfile, 1 );
    if( argc != 2 || !image.data )
    {
        printf( "\n No image data \n " );
        return -1;
    }
    cn=image.channels();
    intensity = image.at<Vec3b>(100, 100);
    printf("\npixel:%d_%d_%d\n",intensity.val[0],intensity.val[1],intensity.val[2]);
    printf("\nThis image has %d rows %d columns and channels=%d\n",image.rows,image.cols,cn);
    cvtColor(image, gray_image, CV_BGR2GRAY );
    printf("\nChannels in gray image=%d\n",gray_image.channels());
    printf("\nValue at that pixel in gray image is %u\n",(int)gray_image.at<uchar>(100,100));
    namedWindow( strimgfile, CV_WINDOW_AUTOSIZE );
    imshow( strimgfile, image );
    waitKey(0);

    return 0;
}

I compile it using

$ g++ code.c -o bincode  -I /usr/include/opencv -I /usr/include/opencv2/imgproc/  -lm `pkg-config --libs --cflags opencv` -ldl

My output is

the file that will be read _image-1.png_

pixel:45_41_31

This image has 240 rows 352 columns and channels=3

Channels in gray image=1

Value at that pixel in gray image is 38

QUE) 45+41+31=117 so its one third is 39 . why do I get 38 ?
QUE)Also please suggest me compilation options or code changes for better performance .I am sure , i am using too many resources for this simple task .

thanks.