This should be the first one hundred terms (if I got the LaTeX magic right):

$$\frac{0}{1}, \frac{1}{1}, \frac{1}{2}, \frac{2}{1}, \frac{1}{3}, \frac{3}{2}, \frac{2}{3}, \frac{3}{1}, \frac{1}{4}, \frac{4}{3}, \frac{3}{5}, \frac{5}{2}, \frac{2}{5}, \frac{5}{3}, \frac{3}{4}, \frac{4}{1}, \frac{1}{5}, \frac{5}{4}, \frac{4}{7}, \frac{7}{3}, \frac{3}{8}, \frac{8}{5}, \frac{5}{7}, \frac{7}{2}, \frac{2}{7}, \frac{7}{5}, \frac{5}{8},$$

$$\frac{8}{3}, \frac{3}{7}, \frac{7}{4}, \frac{4}{5}, \frac{5}{1}, \frac{1}{6}, \frac{6}{5}, \frac{5}{9}, \frac{9}{4}, \frac{4}{11}, \frac{11}{7}, \frac{7}{10}, \frac{10}{3}, \frac{3}{11}, \frac{11}{8}, \frac{8}{13}, \frac{13}{5}, \frac{5}{12}, \frac{12}{7}, \frac{7}{9}, \frac{9}{2}, \frac{2}{9}, \frac{9}{7}, \frac{7}{12}, \frac{12}{5},$$

$$\frac{5}{13}, \frac{13}{8}, \frac{8}{11}, \frac{11}{3}, \frac{3}{10}, \frac{10}{7}, \frac{7}{11}, \frac{11}{4}, \frac{4}{9}, \frac{9}{5}, \frac{5}{6}, \frac{6}{1}, \frac{1}{7}, \frac{7}{6}, \frac{6}{11}, \frac{11}{5}, \frac{5}{14}, \frac{14}{9}, \frac{9}{13}, \frac{13}{4}, \frac{4}{15}, \frac{15}{11}, \frac{11}{18}, \frac{18}{7},$$

$$\frac{7}{17}, \frac{17}{10}, \frac{10}{13}, \frac{13}{3}, \frac{3}{14}, \frac{14}{11}, \frac{11}{19}, \frac{19}{8}, \frac{8}{21}, \frac{21}{13}, \frac{13}{18}, \frac{18}{5}, \frac{5}{17}, \frac{17}{12}, \frac{12}{19}, \frac{19}{7}, \frac{7}{16}, \frac{16}{9}, \frac{9}{11}, \frac{11}{2}, \frac{2}{11}, \frac{11}{9}, \frac{9}{16}, \frac{16}{7}$$