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Now that your question is clear, I can give you an answer:

cv::RNG rng(cv::getTickCount()); // for having each time different numbers
int lo = 16;
int hi = 150; // maximum distance between points: sqrt(3800*2800/300)=188
std::vector< uchar > distantPixels;
cv::Point currentPos(0,0);
while (currentPos.y < image.rows)
{
    while (currentPos.x < image.cols)
    {
        currentPos.x += rng.uniform(lo, hi);
        distantPixel.push_back(image.ptr< uchar >(currentPos.y)[currentPos.x]);
    }
    currentPos.x = 0;
    currentPos.y += rng.uniform(lo, hi);
}

PS: I did not tested it, sorry if it has some bugs, but you get the idea ;)

Now that your question is clear, I can give you an answer:

cv::RNG rng(cv::getTickCount()); // for having each time different numbers
int lo = 16;
int hi = 150; max(16, sqrt(image.cols * image.rows / 300) - 1); // maximum distance between points: sqrt(3800*2800/300)=188
points
std::vector< uchar > distantPixels;
cv::Point currentPos(0,0);
while (currentPos.y < image.rows)
{
    while (currentPos.x < image.cols)
    {
        currentPos.x += rng.uniform(lo, hi);
distantPixel.push_back(image.ptr< uchar >(currentPos.y)[currentPos.x]);
 distantPixel.push_back(image.ptr< uchar >(currentPos.y)[currentPos.x]);
currentPos.x += rng.uniform(lo, hi);
    }
    currentPos.x = 0;
    currentPos.y += rng.uniform(lo, hi);
}

PS: I did not tested it, sorry if it has some bugs, but you get the idea ;)