Hough transform for lines with slope defined by a pair of co-primes

Data structure and Hough-type algorithm suitable for finding the lines having the slope exactly specified by the ratio of small co-prime numbers is proposed. It is suitable for analysing images like the Ulam square in which the points representing prime numbers form such structures as contiguous lines and other regular sequences of points. This analysis is different from that in the case of images in which the real-world objects are represented approximately. Until now in the Ulam square the horizontal and vertical sequences, and those inclined by 45 deg were typically analysed. With the proposed method the sequences having slopes represented by such tangents like 1/3, 2/3, 3/4 etc. can be looked for.