some silly Clojure to explore continued fractions

everything-10.txt

twitter_continued_fraction_spike.clj

And then here is a larger sample, still random and silly.

user => (def samples (distinct (repeatedly 100000 #(shuffle x10))))
;; #'user/samples
user=> (count samples)
;; 98683
user=> (take 50 (sort-by val > (frequencies (sort (map (fn [v] (apply ten-frac v)) samples)))))
;; ([21/2 14] [9N 10] [35/3 9] [11N 9] [33/5 8] [71/11 8] [41/4 8] [52/5 8] [17/3 8] [25/3 8] [31/3 8] [57/7 8] [38/5 7] [67/8 7] [15/2 7] [74/7 7] [13/3 7] [191/17 7] [13/2 7] [19/2 7] [6 7] [17/2 7] [23/3 7] [12 7] [48/7 7] [5 7] [29/4 7] [26/3 7] [171/23 7] [53/8 7] [71/7 6] [153/25 6] [145/17 6] [37/4 6] [177/19 6] [253/31 6] [39/4 6] [32/3 6] [104/11 6] [137/13 6] [66/7 6] [4N 6] [187/19 6] [97/11 6] [179/25 6] [43/6 6] [188/17 6] [149/27 6] [70/9 6] [54/5 6])

Finally learned how to launch a clj session with an external library; forgive me, reader, I am old and from the lein era.

clj -Sdeps "{:deps {org.clojure/math.combinatorics {:mvn/version \"0.1.6\"}}}"

user=> (require '[clojure.math.combinatorics :as combo])
;; nil
user=> (combo/permutations [1 2 3])
;; ([1 2 3] [1 3 2] [2 1 3] [2 3 1] [3 1 2] [3 2 1])
user=> (def all-tens (combo/permutations x10))
;; #'user/all-tens
user=> (take 1000 (sort-by val > (frequencies (sort (map (fn [v] (apply ten-frac v)) all-tens)))))
;; ([9N 430] [11N 380] [7N 322] [21/2 306] [31/3 262] [17/2 258] [15/2 254] [5N 252] [25/3 246] [8N 238] [22/3 218] [51/5 208] [28/3 208] [32/3 206] [17/3 206] [23/3 206] [29/3 206] [13/2 202] [6N 202] [71/7 196] [10N 192] [41/5 182] [59/7 182] [35/3 180] [43/4 180] [19/3 180] [19/2 180] [3N 180] [47/5 178] [57/7 178] [37/4 176] [39/4 176] [53/5 176] [54/5 176] [66/7 174] [48/5 174] [65/7 172] [41/4 172] [20/3 170] [33/4 166] [45/4 164] [43/5 164] [95/9 164] [33/5 162] [23/2 162] [42/5 160] [34/3 158] [74/7 158] [12N 158] [29/4 158] [26/3 158] [103/11 156] [67/7 154] [73/7 154] [53/7 152] [49/5 152] [56/5 152] [75/7 150] [62/7 150] [69/7 148] [44/5 148] [54/7 148] [87/8 148] [52/5 146] [58/7 146] [37/5 144] [61/7 144] [75/8 142] [21/4 142] [31/5 142] [25/4 142] [57/5 140] [36/5 138] [76/7 138] [101/11 138] [51/7 138] [16/3 136] [95/11 136] [4 134] [64/7 134] [91/9 134] [38/7 132] [13/3 132] [94/11 132] [83/9 132] [61/6 132] [33/7 130] [35/4 130] [11/3 130] [67/9 130] [19/4 130] [111/13 128] [38/5 128] [43/7 128] [55/6 128] [92/9 128] [83/11 128] [25/2 128] [69/8 126] [23/4 126] [60/7 126] [46/5 124] [27/4 124] [177/17 122] [32/5 122] [37/3 122] [97/11 122] [93/11 122] [80/7 122] [171/17 122] [117/11 122] [45/7 120] [159/17 120] [85/11 120] [73/8 118] [177/19 118] [72/7 118] [21/5 118] [115/11 118] [114/11 118] [81/11 118] [113/11 118] [135/13 116] [141/17 116] [145/13 116] [173/17 116] [27/5 116] [7/3 114] [77/9 114] [79/7 114] [100/9 114] [17/5 114] [109/13 112] [7/2 112] [65/6 112] [240/23 112] [132/13 112] [134/13 112] [24/5 112] [59/5 112] [86/9 112] [141/13 110] [41/6 110] [91/11 110] [95/13 110] [85/9 110] [73/11 108] [79/11 108] [77/8 108] [47/9 108] [97/9 108] [9/2 108] [157/19 108] [129/17 108] [122/11 108] [123/13 108] [122/13 108] [173/21 108] [30/7 108] [87/11 108] [37/7 106] [39/5 106] [105/11 106] [104/11 106] [107/13 106] [47/6 106] [78/7 106] [43/6 106] [13N 106] [63/11 106] [124/11 106] [31/4 106] [233/23 106] [105/13 104] [137/13 104] [76/9 104] [131/13 104] [123/11 104] [59/8 104] [52/7 104] [120/13 104] [165/16 104] [29/5 104] [51/8 104] [144/13 104] [39/7 102] [107/11 102] [140/13 102] [37/6 102] [13/4 102] [46/7 102] [71/11 102] [14/3 102] [81/13 102] [55/9 102] [146/17 100] [47/11 100] [79/9 100] [11/2 100] [188/17 100] [69/11 100] [11/4 100] [59/9 100] [169/17 100] [68/7 98] [65/9 98] [59/11 98] [55/7 98] [89/9 98] [89/8 98] [124/13 98] [119/11 98] [85/8 98] [58/5 98] [211/19 96] [108/13 96] [106/13 96] [138/13 96] [8/3 96] [102/11 96] [121/13 96] [61/5 96] [49/8 96] [83/8 96] [113/13 96] [147/13 96] [41/9 94] [143/15 94] [110/13 94] [67/6 94] [139/13 94] [64/9 94] [15/4 94] [159/19 94] [157/17 94] [129/13 94] [163/17 94] [16/5 94] [81/7 94] [125/11 94] [48/7 94] [94/9 94] [201/19 94] [173/19 94] [179/17 92] [109/11 92] [183/17 92] [47/4 92] [192/19 92] [29/9 92] [17/4 92] [50/7 92] [49/9 92] [81/8 92] [148/13 92] [119/13 92] [237/23 92] [53/8 92] [118/11 92] [73/9 90] [210/19 90] [79/8 90] [182/17 90] [122/17 90] [97/19 90] [56/11 90] [120/11 90] [93/10 90] [112/13 90] [25/7 90] [25/6 90] [26/5 90] [116/11 90] [74/9 88] [176/21 88] [180/17 88] [108/11 88] [13/5 88] [93/13 88] [125/13 88] [195/19 88] [167/19 88] [165/17 88] [82/7 88] [198/19 88] [267/29 88] [153/14 88] [174/19 88] [247/23 86] [319/31 86] [106/11 86] [34/7 86] [78/11 86] [111/10 86] [185/17 86] [187/18 86] [67/8 86] [101/9 86] [99/13 86] [101/10 86] [57/11 86] [89/11 86] [53/6 86] [94/13 86] [61/9 86] [123/14 86] [126/11 86] [105/17 86] [82/11 86] [86/11 86] [174/17 86] [251/24 84] [111/11 84] [5/2 84] [97/10 84] [125/17 84] [158/19 84] [41/7 84] [29/8 84] [89/12 84] [63/8 84] [51/10 84] [106/17 84] [175/17 84] [145/17 82] [79/13 82] [183/19 82] [133/13 82] [131/11 82] [10/3 82] [65/8 82] [123/17 82] [64/11 82] [273/29 82] [68/9 82] [278/27 82] [100/11 82] [126/13 82] [193/21 82] [61/8 82] [192/23 82] [137/17 82] [87/13 82] [118/13 82] [112/11 82] [150/13 82] [113/12 82] [115/13 82] [246/23 80] [36/7 80] [242/23 80] [32/7 80] [47/7 80] [102/13 80] [163/15 80] [96/13 80] [71/8 80] [23/7 80] [23/5 80] [58/9 80] [135/19 80] [31/10 80] [17/7 80] [51/11 80] [151/15 80] [29/7 80] [139/17 80] [80/11 80] [291/29 80] [114/13 80] [144/17 78] [178/19 78] [38/3 78] [181/19 78] [146/21 78] [67/11 78] [275/27 78] [37/9 78] [219/23 78] [103/10 78] [127/17 78] [39/8 78] [40/7 78] [128/15 78] [163/19 78] [58/11 78] [90/11 78] [31/11 78] [18/7 78] [92/11 78] [49/11 78] [171/23 78] [84/11 78] [146/13 78] [168/23 78] [109/15 76] [45/8 76] [45/11 76] [34/5 76] [98/11 76] [44/7 76] [67/13 76] [71/9 76] [189/19 76] [68/11 76] [61/13 76] [57/8 76] [195/17 76] [155/14 76] [18/5 76] [295/29 76] [258/25 76] [234/23 76] [78/17 76] [110/17 76] [179/19 74] [74/11 74] [107/10 74] [247/22 74] [41/11 74] [79/12 74] [87/19 74] [211/23 74] [249/29 74] [281/29 74] [72/13 74] [182/19 74] [241/23 74] [342/31 74] [101/14 74] [70/11 74] [69/10 74] [70/9 74] [97/17 74] [199/23 74] [303/31 74] [337/33 74] [165/23 74] [163/16 74] [49/4 74] [194/23 74] [19/5 74] [197/19 74] [257/23 74] [49/6 74] [107/17 74] [259/25 74] [62/5 74] [81/10 74] [82/9 74] [169/18 74] [200/19 74] [235/23 74] [142/17 74] [113/17 72] [181/21 72] [425/41 72] [43/9 72] [147/17 72] [181/17 72] [151/17 72] [46/9 72] [76/11 72] [98/9 72] [186/17 72] [186/23 72] [243/29 72] [263/23 72] [373/37 72] [341/37 72] [96/19 72] [63/10 72] [61/11 72] [101/19 72] [193/23 72] [62/9 72] [327/31 72] [31/6 72] [28/5 72] [351/37 72] [142/19 72] [205/19 72] [232/23 72] [177/16 70] [145/19 70] [40/11 70] [73/10 70] [115/16 70] [73/13 70] [139/15 70] [399/41 70] [136/15 70] [123/19 70] [12/5 70] [103/14 70] [153/16 70] [61/17 70] [97/13 70] [71/10 70] [97/12 70] [215/26 70] [127/15 70] [125/12 70] [131/17 70] [229/23 70] [89/13 70] [199/19 70] [29/11 70] [196/19 70] [31/7 70] [203/19 70] [84/13 70] [80/9 70] [116/13 70] [195/31 70] [53/11 70] [141/19 70] [113/14 70] [77/12 68] [283/26 68] [215/21 68] [253/31 68] [147/16 68] [15/7 68] [35/11 68] [120/17 68] [222/23 68] [120/19 68] [131/15 68] [189/17 68] [191/17 68] [391/41 68] [98/13 68] [131/19 68] [161/17 68] [160/17 68] [85/7 68] [197/23 68] [59/13 68] [207/25 68] [28/11 68] [169/16 68] [202/19 68] [137/19 68] [140/17 68] [53/10 68] [115/12 68] [176/17 66] [115/17 66] [141/14 66] [73/12 66] [79/10 66] [118/19 66] [211/22 66] [47/8 66] [77/10 66] [137/14 66] [121/17 66] [187/19 66] [33/8 66] [101/12 66] [133/12 66] [91/17 66] [103/13 66] [179/25 66] [90/17 66] [189/22 66] [39/11 66] [9/4 66] [128/13 66] [272/29 66] [66/13 66] [92/13 66] [198/23 66] [192/17 66] [63/13 66] [127/13 66] [239/29 66] [57/10 66] [19/7 66] [83/7 66] [133/17 66] [93/8 66] [166/19 66] [165/19 66] [167/17 66] [331/29 66] [89/14 66] [134/17 66] [85/13 66] [50/11 66] [106/19 66] [137/16 66] [29/6 66] [48/11 66] [53/9 66] [21/8 66] [59/6 66] [170/23 66] [172/17 66] [232/21 66] [24/7 66] [55/8 66] [204/19 66] [249/25 64] [109/12 64] [213/23 64] [601/59 64] [72/11 64] [41/13 64] [107/15 64] [106/15 64] [248/29 64] [117/19 64] [283/29 64] [331/35 64] [121/16 64] [135/14 64] [130/11 64] [254/23 64] [309/31 64] [311/29 64] [154/17 64] [310/29 64] [191/19 64] [156/17 64] [95/17 64] [97/15 64] [327/41 64] [156/19 64] [339/35 64] [162/19 64] [19/6 64] [134/19 64] [196/17 64] [330/31 64] [413/43 64] [17/6 64] [267/28 64] [239/23 64] [85/12 64] [19/8 64] [224/27 64] [83/13 64] [143/17 64] [111/16 64] [165/26 64] [79/15 62] [121/25 62] [357/37 62] [3/2 62] [150/23 62] [214/23 62] [359/37 62] [43/8 62] [148/23 62] [35/6 62] [101/13 62] [153/19 62] [70/13 62] [11/5 62] [217/23 62] [67/12 62] [278/25 62] [226/19 62] [269/31 62] [127/12 62] [235/31 62] [265/29 62] [297/29 62] [135/17 62] [83/10 62] [202/17 62] [175/19 62] [80/13 62] [87/10 62] [141/16 62] [111/17 62] [113/15 62] [169/23 62] [170/21 62] [172/19 62] [256/31 62] [81/17 60] [75/11 60] [253/29 60] [251/27 60] [145/16 60] [147/23 60] [399/43 60] [385/37 60] [40/13 60] [137/15 60] [54/17 60] [151/16 60] [89/17 60] [67/10 60] [166/15 60] [35/9 60] [155/17 60] [99/14 60] [37/11 60] [133/11 60] [34/13 60] [36/11 60] [126/17 60] [158/17 60] [27/11 60] [197/21 60] [345/41 60] [23/6 60] [91/10 60] [232/25 60] [161/19 60] [89/10 60] [160/19 60] [229/22 60] [230/21 60] [69/17 60] [195/23 60] [197/17 60] [103/17 60] [90/13 60] [135/16 60] [269/26 60] [139/19 60] [55/13 60] [116/15 60] [117/14 60] [260/31 60] [115/14 60] [201/20 60] [231/25 60] [257/31 60] [175/16 60] [153/25 58] [393/41 58] [42/11 58] [41/8 58] [115/18 58] [251/26 58] [47/13 58] [83/17 58] [117/23 58] [142/13 58] [176/19 58] [315/31 58] [46/11 58] [117/16 58] [107/14 58] [136/13 58] [181/16 58] [346/31 58] [178/21 58] [180/19 58] [57/17 58] [90/19 58] [122/19 58] [158/23 58] [159/22 58] [189/20 58] [208/25 58] [65/11 58] [125/23 58] [121/19 58] [183/29 58] [277/25 58] [98/15 58] [306/29 58] [25/8 58] [86/7 58] [96/17 58] [129/16 58] [27/8 58] [162/17 58] [267/31 58] [88/13 58] [121/12 58] [161/20 58] [298/31 58] [297/28 58] [121/15 58] [51/4 58] [143/23 58] [381/37 58] [170/19 58] [108/23 58] [113/10 58] [149/14 58] [162/25 58] [171/16 58] [111/19 58] [109/17 58] [143/19 58] [161/29 58] [309/41 58] [345/37 58] [321/31 58] [145/14 58] [171/20 58] [197/26 58] [378/37 58] [283/27 56] [317/29 56] [183/22 56] [181/22 56] [149/17 56] [189/25 56] [44/9 56] [148/17 56] [179/22 56] [177/23 56] [179/21 56] [219/29 56] [253/27 56] [148/19 56] [218/29 56] [212/19 56] [167/15 56] [277/29 56] [343/31 56] [99/10 56] [13/6 56] [103/12 56] [96/11 56] [93/17 56] [183/25 56] [357/43 56] [367/33 56] [329/39 56] [218/21 56] [201/25 56] [231/23 56] [229/21 56] [56/9 56] [88/9 56] [268/29 56] [477/47 56] [553/59 56] [124/15 56] [234/25 56] [28/9 56] [67/21 56] [329/31 56] [194/21 56] [348/43 56] [53/13 56] [73/17 56] [149/13 56] [27/2 56] [87/14 56] [172/21 56] [198/31 56] [238/23 56] [169/19 56] [197/31 56] [107/16 56] [138/17 56] [168/19 56] [45/17 56] [207/19 56] [54/11 56] [206/19 56] [23/9 56] [79/17 56] [229/27 56] [143/16 56] [149/21 54] [183/23 54] [215/23 54] [291/35 54] [399/47 54] [281/27 54] [179/16 54] [230/37 54] [390/37 54] [117/17 54] [151/19 54] [323/39 54] [47/10 54] [154/31 54] [157/24 54] [5/3 54] [75/13 54] [149/19 54] [169/15 54] [315/29 54] [86/17 54] [127/23 54] [155/19 54] [181/29 54] [88/17 54] [100/13 54] [184/17 54] [211/25 54] [83/24 54] [448/43 54] [149/25 54] [213/25 54] [483/47 54] [38/11 54] [37/8 54] [123/22 54] [217/20 54] [103/9 54] [185/23 54] [277/27 54] [131/12 54] [247/24 54] [480/47 54] [25/9 54] [169/24 54] [167/22 54] [193/19 54] [261/23 54] [95/12 54] [99/16 54] [196/23 54] [194/17 54] [37/17 54] [57/13 54] [91/15 54] [163/23 54] [237/25 54] [447/43 54] [69/19 54] [299/29 54] [91/12 54] [103/16 54] [237/26 54] [113/9 54] [231/31 54] [313/33 54] [337/41 54] [429/53 54] [168/17 54] [251/34 54] [294/31 54] [149/15 54] [205/23 54] [339/41 54] [407/43 54] [224/29 54] [228/25 54] [283/37 54] [411/37 54] [485/59 54] [23/8 54] [82/13 54] [140/19 54] [119/23 52] [159/31 52] [79/14 52] [262/39 52] [81/19 52] [245/23 52] [82/17 52] [52/17 52] [149/16 52] [223/26 52] [314/31 52] [123/29 52] [293/35 52] [241/22 52] [63/23 52] [209/25 52] [223/23 52] [68/13 52] [190/23 52] [93/23 52] [189/23 52] [221/23 52] [40/3 52] [148/31 52] [176/27 52] [188/23 52] [187/16 52] [216/19 52] [270/37 52] [187/23 52] [251/23 52] [64/13 52] [212/25 52] [333/32 52] [333/35 52] [65/14 52] [187/20 52] [99/19 52] [157/13 52] [447/47 52] [61/12 52] [61/15 52] [173/31 52] [207/29 52] [158/13 52] [236/31 52] [103/19 52] [231/19 52] [2N 52] [122/15 52])

Also interesting:

There are 10! different assignments possible (in all-tens, above) but

user=> (count (frequencies (sort (map (fn [v] (apply ten-frac v)) all-tens))))
;; 1198543