Size article thumbnails and retrieve them directly from database

I’ve integrated the WordPress database directly with my .NET application.

What I want is to set the featured image of a post. This featured image must be maximum 800pixels wide, and automatically sized to that width (keeping the correct width/height ratio).

Medium size is set tp 300×300
Large size is set to 1024×1024

What I did now is go to Settings > Media and set the width of Thumbnail size to 600 and unchecked the checkbox Crop thumbnail to exact dimensions (normally thumbnails are proportional).

Now when I upload a new featured image, where can I find the filename of the image with a width of 600px and how can I retrieve it via SQL?

UPDATE

I see these rows in [wp_postmeta]

meta_id post_id meta_key                meta_value
76      16      _wp_attached_file       2014/01/sitelargeblah.png
77      16      _wp_attachment_metadata a:5:{s:5:"width";i:1920;s:6:"height";i:1643;s:4:"file";s:25:"2014/01/sitelargeblah.png";s:5:"sizes";a:4:{s:9:"thumbnail";a:4:{s:4:"file";s:25:"sitelargeblah-175x150.png";s:5:"width";i:175;s:6:"height";i:150;s:9:"mime-type";s:9:"image/png";}s:6:"medium";a:4:{s:4:"file";s:25:"sitelargeblah-300x256.png";s:5:"width";i:300;s:6:"height";i:256;s:9:"mime-type";s:9:"image/png";}s:5:"large";a:4:{s:4:"file";s:26:"sitelargeblah-1024x876.png";s:5:"width";i:1024;s:6:"height";i:876;s:9:"mime-type";s:9:"image/png";}s:14:"post-thumbnail";a:4:{s:4:"file";s:25:"sitelargeblah-604x270.png";s:5:"width";i:604;s:6:"height";i:270;s:9:"mime-type";s:9:"image/png";}}s:10:"image_meta";a:10:{s:8:"aperture";i:0;s:6:"credit";s:0:"";s:6:"camera";s:0:"";s:7:"caption";s:0:"";s:17:"created_timestamp";i:0;s:9:"copyright";s:0:"";s:12:"focal_length";i:0;s:3:"iso";i:0;s:13:"shutter_speed";i:0;s:5:"title";s:0:"";}}

I see the 300px width and the 1024px width, but no 800px width of the thumbnail. Why not?

I can not simply append 800×800 after the value in _wp_attached_file, since the resized image is not an exact square, but with dimensions ratios preserved.