games with numbers

I was watching videos about Collatz and these thoughts occurred to me.

There are more interesting graphs around a julia set like set up.

 

n 1 2 3 4 5 6 7 8 9 10
n^2 1 4 9 16 25 36 49 64 81 100
3(n)+1 4 7 10 13 16 19 22 25 28 31
(3(n+1))/2 2 3.5 5 6.5 8 9.5 11 12.5 14 15.5
subtract 3 5 7 9 11 13 15 17 19 21
tot/n 4 3.5 3.33333333333333 3.25 3.2 3.16666666666667 3.14285714285714 3.125 3.11111111111111 3.1
n/tot 0.5 0.571428571428571 0.6 0.615384615384615 0.625 0.631578947368421 0.636363636363636 0.64 0.642857142857143 0.645161290322581
n 11 12 13 14 15 16 17 18 19 20
n^2 121 144 169 196 225 256 289 324 361 400
3(n)+1 34 37 40 43 46 49 52 55 58 61
(3(n+1))/2 17 18.5 20 21.5 23 24.5 26 27.5 29 30.5
subtract 23 25 27 29 31 33 35 37 39 41
tot/n 3.09090909090909 3.08333333333333 3.07692307692308 3.07142857142857 3.06666666666667 3.0625 3.05882352941176 3.05555555555556 3.05263157894737 3.05
n/tot 0.647058823529412 0.648648648648649 0.65 0.651162790697674 0.652173913043478 0.653061224489796 0.653846153846154 0.654545454545455 0.655172413793103 0.655737704918033
n 21 22 23 24 25 26 27 28 29 30
n^2 441 484 529 576 625 676 729 784 841 900
3(n)+1 64 67 70 73 76 79 82 85 88 91
(3(n+1))/2 32 33.5 35 36.5 38 39.5 41 42.5 44 45.5
subtract 43 45 47 49 51 53 55 57 59 61
tot/n 3.04761904761905 3.04545454545455 3.04347826086957 3.04166666666667 3.04 3.03846153846154 3.03703703703704 3.03571428571429 3.03448275862069 3.03333333333333
n/tot 0.65625 0.656716417910448 0.657142857142857 0.657534246575342 0.657894736842105 0.658227848101266 0.658536585365854 0.658823529411765 0.659090909090909 0.659340659340659
n 31 32 33 34 35 36 37 38 39 40
n^2 961 1024 1089 1156 1225 1296 1369 1444 1521 1600
3(n)+1 94 97 100 103 106 109 112 115 118 121
(3(n+1))/2 47 48.5 50 51.5 53 54.5 56 57.5 59 60.5
subtract 63 65 67 69 71 73 75 77 79 81
tot/n 3.03225806451613 3.03125 3.03030303030303 3.02941176470588 3.02857142857143 3.02777777777778 3.02702702702703 3.02631578947368 3.02564102564103 3.025
n/tot 0.659574468085106 0.65979381443299 0.66 0.660194174757282 0.660377358490566 0.660550458715596 0.660714285714286 0.660869565217391 0.661016949152542 0.661157024793388
n 41 42 43 44 45 46 47 48 49 50
n^2 1681 1764 1849 1936 2025 2116 2209 2304 2401 2500
3(n)+1 124 127 130 133 136 139 142 145 148 151
(3(n+1))/2 62 63.5 65 66.5 68 69.5 71 72.5 74 75.5
subtract 83 85 87 89 91 93 95 97 99 101
tot/n 3.02439024390244 3.02380952380952 3.02325581395349 3.02272727272727 3.02222222222222 3.02173913043478 3.02127659574468 3.02083333333333 3.02040816326531 3.02
n/tot 0.661290322580645 0.661417322834646 0.661538461538462 0.661654135338346 0.661764705882353 0.661870503597122 0.661971830985916 0.662068965517241 0.662162162162162 0.662251655629139
n 51 52 53 54 55 56 57 58 59 60
n^2 2601 2704 2809 2916 3025 3136 3249 3364 3481 3600
3(n)+1 154 157 160 163 166 169 172 175 178 181
(3(n+1))/2 77 78.5 80 81.5 83 84.5 86 87.5 89 90.5
subtract 103 105 107 109 111 113 115 117 119 121
tot/n 3.01960784313725 3.01923076923077 3.0188679245283 3.01851851851852 3.01818181818182 3.01785714285714 3.01754385964912 3.01724137931034 3.01694915254237 3.01666666666667
n/tot 0.662337662337662 0.662420382165605 0.6625 0.662576687116564 0.662650602409639 0.662721893491124 0.662790697674419 0.662857142857143 0.662921348314607 0.662983425414365
n 61 22 23 24 25 26 27 28 29 30
n^2 3721 484 529 576 625 676 729 784 841 900
3(n)+1 184 67 70 73 76 79 82 85 88 91
(3(n+1))/2 92 33.5 35 36.5 38 39.5 41 42.5 44 45.5
subtract 123 45 47 49 51 53 55 57 59 61
tot/n 3.01639344262295 3.04545454545455 3.04347826086957 3.04166666666667 3.04 3.03846153846154 3.03703703703704 3.03571428571429 3.03448275862069 3.03333333333333
n/tot 0.663043478260869 0.656716417910448 0.657142857142857 0.657534246575342 0.657894736842105 0.658227848101266 0.658536585365854 0.658823529411765 0.659090909090909 0.659340659340659
n 31 32 33 34 35 36 37 38 39 40
n^2 961 1024 1089 1156 1225 1296 1369 1444 1521 1600
3(n)+1 94 97 100 103 106 109 112 115 118 121
(3(n+1))/2 47 48.5 50 51.5 53 54.5 56 57.5 59 60.5
subtract 63 65 67 69 71 73 75 77 79 81
tot/n 3.03225806451613 3.03125 3.03030303030303 3.02941176470588 3.02857142857143 3.02777777777778 3.02702702702703 3.02631578947368 3.02564102564103 3.025
n/tot 0.659574468085106 0.65979381443299 0.66 0.660194174757282 0.660377358490566 0.660550458715596 0.660714285714286 0.660869565217391 0.661016949152542 0.661157024793388

Author: ompaul

Usually I am found in Ireland.

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