## Saturday, March 14, 2020

### [xzgsyzcv] Approximately equally spaced rational slopes

Below are continued fraction representations of slopes of selected angles between 0 and 45 degrees.  Truncate and compute a convergent according to your desired precision.  The selected angles are the integer degrees (because 360 is a nice number) and the multiples of Pi/256 radian = (180/256 = 45/64 = 0.703125) degree (because binary is nice).

For angles between 45 and 90, take the reciprocal.

Not sure what this might be useful for.  It's aesthetically elegant to represent a slope as a fraction.

Quadratic surds at 15, 22.5, and 30 degree, visible as repeating terms.

Let phi be the golden ratio 1.618.  In the vicinity of Pi/2-atan(phi) radian, or 31.72 degree, the slope is 1/phi (or phi-1), so it takes many continued fraction terms to distinguish nearby slopes, as the leading terms are all ones.

tan(31 degree 43 minute (2 + 54/60) second) =
{0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 3, 3, 2, 3, 9, 2, 15}

{0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 2, 2, 1, 5, 1, 3, 5, 1, 3, 1, 1}

tan(1.40625 degree) = tan(Pi/128 radian) is very close to 155/6314, truncating just before the large term 37310 (the largest term seen in the table below).  Or, 128*atan(155/6314) differs from Pi by 8.59994e-11.

In the table below, the first term is the angle in degrees, then it is followed by 30 terms in curly braces of the continued fraction of the slope of the angle.  The table was generated using Mathematica.  For example, here is Mathematica code for the multiples of Pi/256 radian:

vmax:=2^8; Do[Print[ContinuedFraction[Tan[n*Pi/vmax],30]], {n,1,vmax/4-1}]

0.703125 {0, 81, 2, 14, 2, 2, 2, 460, 1, 3, 1, 4, 2, 2, 7, 2, 1, 1, 94, 2, 1, 8, 1, 1, 2, 23, 1, 32, 1, 9}

1 {0, 57, 3, 2, 4, 2, 1, 1, 1, 10, 1, 15, 1, 12, 2, 4, 1, 7, 3, 9, 1, 1, 2, 3, 7, 2, 1, 2, 1, 9}

1.40625 {0, 40, 1, 2, 1, 3, 1, 1, 3, 1, 37310, 1, 4, 6, 54, 2, 13, 5, 1, 284, 1, 1, 2, 2, 1, 1, 12, 3, 2, 1}

2 {0, 28, 1, 1, 1, 2, 1, 74, 6, 8, 1, 4, 6, 1, 1, 2, 9, 2, 3, 1, 17, 6, 1, 1, 5, 1, 1, 1, 29, 2}

2.109375 {0, 27, 6, 1, 1, 1, 13, 1, 674, 1, 9, 4, 2, 1, 4, 1, 71, 2, 2, 1, 2, 1, 1, 2, 1, 4, 1, 8, 2, 1}

2.8125 {0, 20, 2, 1, 4, 2, 1, 4, 1, 12, 1, 2, 1, 4, 1, 13, 8, 1, 1, 1, 8, 1, 2, 1, 5, 1, 2, 11, 2, 1}

3 {0, 19, 12, 3, 12, 1, 4, 3, 5, 1, 34, 2, 2, 3, 1, 21, 1, 3, 1, 1, 6, 4, 4, 1, 2, 4, 1, 1, 3, 6}

3.515625 {0, 16, 3, 1, 1, 1, 1, 3, 2, 1, 1, 21, 3, 5, 2, 10, 1, 28, 34, 2, 1, 2, 62, 4, 3, 13, 1, 4, 2, 2}

4 {0, 14, 3, 3, 14, 1, 2, 2, 3, 1, 1, 1, 1, 4, 1, 1, 10, 3, 3, 1, 7, 2, 4, 1, 1, 1, 1, 24, 2, 8}

4.21875 {0, 13, 1, 1, 3, 1, 10, 3, 3, 1, 104, 2, 2, 35, 2, 9, 17, 4, 5, 12, 1, 2, 1, 661, 4, 2, 36, 1, 1, 1}

4.921875 {0, 11, 1, 1, 1, 1, 2, 1, 1, 1, 2, 13, 1, 3, 1, 7, 2, 2, 2, 5, 1, 1, 3, 124, 2, 4, 1, 1, 1, 1}

5 {0, 11, 2, 3, 13, 2, 54, 2, 1, 1, 2, 3, 2, 33, 2, 2, 1, 3, 1, 48, 6, 4, 1, 2, 8, 4, 1, 3, 1, 2}

5.625 {0, 10, 6, 1, 1, 8, 4, 1, 1, 2, 4, 1, 2, 1, 1, 5, 3, 1, 1, 1, 2, 7, 3, 1, 2, 2, 3, 1, 15, 2}

6 {0, 9, 1, 1, 16, 1, 9, 2, 2, 1, 4, 3, 9, 10, 3, 1, 3, 1, 1, 2, 5, 16, 1, 3, 5, 1, 1, 8, 1, 1}

6.328125 {0, 9, 57, 1, 3, 1, 8, 3, 1, 11, 1, 4, 1, 3, 7, 9, 12, 1, 3, 3, 165, 1, 1, 2, 1, 5, 1, 1, 8, 2}

7 {0, 8, 6, 1, 12, 1, 5, 1, 1, 185, 3, 1, 1, 1, 1, 14, 9, 9, 10, 2, 1, 3, 1, 3, 11, 7, 2, 1, 6, 1}

7.03125 {0, 8, 9, 3, 1, 1, 1, 1, 25, 1, 1, 18, 5, 2, 2, 3, 1, 1, 2, 8, 1, 5, 4, 6, 5, 2, 1, 3, 1, 9}

7.734375 {0, 7, 2, 1, 3, 10, 1, 3, 3, 1, 4, 1, 1, 12, 1, 3, 12, 1, 3, 8, 1, 1, 11, 3, 22, 29, 1, 3, 2, 1}

8 {0, 7, 8, 1, 2, 98, 1, 53, 1, 2, 8, 3, 2, 1, 5, 1, 24, 2, 9, 1, 4, 5, 2, 1, 1, 1, 3, 1, 5, 1}

8.4375 {0, 6, 1, 2, 1, 6, 1, 1, 3, 1, 1, 7, 4, 2, 1, 2, 2, 1, 1, 1, 3, 1, 2, 34, 15, 58, 8, 2, 1, 3}

9 {0, 6, 3, 5, 2, 1, 14, 11, 2, 25, 1, 3, 1, 15, 1, 4, 3, 1, 1, 1, 2, 26, 1, 3, 4, 2, 2, 2, 5, 20}

9.140625 {0, 6, 4, 1, 1, 1, 6, 1, 1, 1, 1, 1, 26, 3, 1, 1, 2, 2, 1, 3, 1, 3, 2, 1, 7, 1, 11, 1, 1, 3}

9.84375 {0, 5, 1, 3, 4, 1, 1, 43, 32, 1, 2, 4, 1, 4, 3, 3, 1, 2, 1, 2, 1, 1, 2, 2, 1, 11, 1, 1, 1, 1}

10 {0, 5, 1, 2, 23, 1, 2, 1, 7, 75, 1, 7, 2, 1, 2, 1, 400, 1, 1, 1, 3, 1, 3, 5, 1, 8, 2, 2, 1, 6}

10.546875 {0, 5, 2, 1, 2, 3, 1, 1, 10, 1, 8, 1, 10, 1, 4, 1, 1, 37, 2, 1, 3, 2, 1, 1, 1, 1, 2, 3, 12, 27}

11 {0, 5, 6, 1, 11, 5, 1, 8, 11, 1, 1, 10, 5, 3, 3, 3, 2, 13, 88, 1, 1, 1, 2, 3, 3, 8, 1, 3, 6, 1}

11.25 {0, 5, 36, 1, 1, 2, 1, 2, 1, 6, 1, 1, 1, 1, 1, 7, 1, 1, 1, 4, 1, 1, 5, 2, 2, 2, 3, 16, 5, 1}

11.953125 {0, 4, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 6, 2, 2, 1, 1, 2, 4, 2, 2, 1, 1, 1, 3, 2, 1, 2}

12 {0, 4, 1, 2, 2, 1, 1, 2, 5, 1, 2, 1, 1, 21, 2, 1, 52, 1, 7, 1, 21, 1, 1, 9, 3, 5, 10, 1, 1, 2}

12.65625 {0, 4, 2, 4, 1, 5, 2, 1, 94, 1, 6, 2, 1, 21, 5, 2, 1, 1, 1, 1, 1, 2, 1, 3, 1, 1, 23, 6, 1, 2}

13 {0, 4, 3, 59, 2, 16, 1, 3, 1, 3, 1, 4, 1, 1, 2, 1, 1, 6, 2, 2, 1, 1, 1, 2, 1, 90, 3, 8, 3, 2}

13.359375 {0, 4, 4, 1, 2, 1, 9, 3, 4, 2, 2, 1, 2, 3, 1, 1, 1, 1, 12, 2, 1, 7, 1, 4, 1, 5, 23, 1, 2, 1}

14 {0, 4, 92, 1, 3, 9, 1, 1, 2, 36, 10, 32, 1, 3, 7, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 18, 3, 1, 4}

14.0625 {0, 3, 1, 127, 1, 1, 2, 14, 7, 1, 2, 5, 1, 1, 1, 1, 6, 12, 1, 6, 6, 1, 13, 2, 3, 5, 1, 1, 1, 3}

14.765625 {0, 3, 1, 3, 1, 5, 1, 15, 10, 1, 2, 6, 2, 6, 4, 1, 2, 14, 2, 15, 5, 4, 5, 15, 1, 60, 1, 5, 1, 1}

15 {0, 3, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2}

15.46875 {0, 3, 1, 1, 1, 1, 2, 2, 1, 4, 2, 2, 1, 6, 2, 22, 1, 28, 4, 1, 4, 2, 6, 5, 18, 4, 2, 10, 1, 2}

16 {0, 3, 2, 19, 2, 1, 2, 1, 19, 1, 2, 2, 6, 1, 1, 1, 5, 1, 3, 4, 609, 2, 2, 3, 1, 1, 15, 2, 13, 1}

16.171875 {0, 3, 2, 4, 2, 1, 17, 1, 11, 3, 1, 2, 3, 5, 2, 1, 1, 1, 5, 1, 1, 1, 1, 3, 1, 2, 8, 1, 13, 3}

16.875 {0, 3, 3, 2, 1, 2, 4, 1, 6, 1, 1, 11, 1, 1, 1, 1, 8, 1, 122, 1, 1, 5, 6, 2, 1, 8, 2, 16, 1, 2}

17 {0, 3, 3, 1, 2, 4, 22, 3, 1, 1, 1, 1, 2, 11, 5, 1, 6, 3, 45, 1, 1, 2, 31, 1, 3, 1, 14, 3, 2, 10}

17.578125 {0, 3, 6, 2, 1, 1, 2, 2, 1, 3, 7, 3, 1, 8, 1, 7, 1, 1, 1, 1, 3, 1, 6, 1, 4, 8, 1, 1, 4, 2}

18 {0, 3, 12, 1, 6, 1, 6, 25, 4, 1, 1, 15, 1, 2, 2, 1, 2, 1, 1, 51, 1, 266, 6, 1, 1, 3, 1, 1, 1, 6}

18.28125 {0, 3, 36, 1, 44, 5, 1, 1, 5, 1, 1, 7, 12, 1, 1, 1, 1, 1, 11, 4, 7, 1, 1, 1, 1, 1, 2, 4, 4, 1}

18.984375 {0, 2, 1, 9, 1, 2, 1, 2, 11, 2, 2, 4, 1, 2, 4, 4, 1, 7, 1, 3, 2, 1, 1, 2, 20, 1, 3, 1, 19, 2}

19 {0, 2, 1, 9, 2, 3, 1, 1, 1, 3, 2, 1, 7, 3, 1, 29, 2, 2, 1, 4, 4, 4, 3, 1, 1, 1, 5, 166, 4, 1}

19.6875 {0, 2, 1, 3, 1, 6, 1, 10, 3, 1, 2, 1, 5, 3, 1, 1, 1, 12, 1, 5, 58, 2, 1, 8, 1, 2, 1, 5, 4, 6}

20 {0, 2, 1, 2, 1, 24, 38, 6, 1, 9, 17, 4, 1, 4, 1, 11, 1, 2, 2, 1, 5, 1, 3, 1, 1, 2, 4, 1, 1, 7}

20.390625 {0, 2, 1, 2, 4, 2, 1, 2, 103, 1, 33, 3, 1, 7, 1, 5, 1, 1, 1, 2, 2, 7, 5, 1, 7, 1, 19, 1, 5, 14}

21 {0, 2, 1, 1, 1, 1, 7, 3, 1, 5, 1, 1, 41, 2, 3, 2, 240, 3, 4, 2, 8, 3, 1, 18, 8, 1142, 1, 1, 5, 2}

21.09375 {0, 2, 1, 1, 2, 4, 1, 6, 2, 2, 19, 4, 3, 1, 1, 1, 9, 1, 1, 5, 2, 4, 3, 1, 3, 1, 3, 2, 13, 3}

21.796875 {0, 2, 1, 1, 435, 8, 6, 1, 29, 2, 1, 1, 2, 32, 1, 6, 2, 3, 3, 1, 2, 7, 1, 24, 1, 1, 4, 1, 4, 1}

22 {0, 2, 2, 9, 1, 1, 6, 1, 2, 25, 8, 1, 1, 8, 10, 1, 1, 1, 4, 3, 8, 5, 2, 6, 4, 2, 1, 4, 7, 24}

22.5 {0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2}

23 {0, 2, 2, 1, 4, 3, 1, 2, 1, 5, 12, 1, 1, 3, 1, 3, 4, 21, 3, 2, 6, 4, 10, 1, 12, 2, 5, 1, 1, 1}

23.203125 {0, 2, 3, 217, 1, 1, 3, 1, 1, 2, 1, 59, 1, 3, 2, 1, 15, 1, 13, 1, 6, 1, 1, 5, 3, 1, 50, 10, 1, 1}

23.90625 {0, 2, 3, 1, 9, 1, 2, 1, 2, 2, 1, 9, 8, 1, 1, 4, 1, 4, 3, 1, 2, 4, 2, 7, 1, 1, 2, 1, 1, 2}

24 {0, 2, 4, 15, 1, 1, 12, 83, 1, 6, 1, 480, 1, 1, 1, 1, 1, 2, 1, 3, 1, 1, 1, 2, 9, 16, 571, 3, 1, 2}

24.609375 {0, 2, 5, 2, 5, 2, 1, 51, 2, 16, 1, 1, 1, 2, 3, 1, 12, 3, 1, 4, 3, 1, 1, 2, 2, 3, 1, 40, 1, 2}

25 {0, 2, 6, 1, 11, 1, 1, 18, 1, 1, 2, 1, 19, 8, 1, 1, 1, 1, 10, 1, 5, 2, 1, 5, 1, 2, 2, 1, 1, 3}

25.3125 {0, 2, 8, 1, 2, 1, 21, 1, 1, 6, 1, 2, 7, 3, 6, 2, 2, 1, 1, 28, 1, 2, 18, 2, 11, 2, 12, 1, 1, 1}

26 {0, 2, 19, 1, 7, 3, 1, 1, 2, 15, 1, 1, 59, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 11, 83, 9}

26.015625 {0, 2, 20, 2, 5, 5, 1, 2, 2, 1, 1, 1, 5, 2, 9, 1, 3, 2, 1, 1, 2, 3, 1, 41, 1, 1, 2, 9, 1, 2}

26.71875 {0, 1, 1, 73, 1, 21, 1, 1, 2, 3, 1, 2, 3, 1, 3, 25, 4, 23, 2, 15, 4, 5, 2, 9, 1, 3, 3, 17, 1, 3}

27 {0, 1, 1, 25, 1, 2, 1, 13, 12, 1, 1, 1, 1, 3, 7, 1, 5, 1, 2, 1, 3, 1, 25, 2, 133, 13, 8, 3, 3, 15}

27.421875 {0, 1, 1, 12, 1, 3, 2, 2, 7, 3, 1, 1, 1, 2, 4, 2, 3, 1, 4, 8, 1, 2, 1, 9, 4, 3, 1, 1, 1, 2}

28 {0, 1, 1, 7, 2, 1, 1, 1, 1, 10, 1, 1, 1, 3, 3, 1, 22, 2, 1, 13, 1, 1, 1, 22, 3, 2, 1, 15, 2, 1}

28.125 {0, 1, 1, 6, 1, 2, 1, 9, 1, 2, 1, 3, 5, 1, 4, 18, 1, 60, 1, 3, 2, 1, 1, 2, 1, 2, 17, 1, 33, 2}

28.828125 {0, 1, 1, 4, 2, 5, 1, 8, 2, 5, 1, 1, 1, 2, 1, 6, 2, 1, 2, 4, 1, 2, 3, 3, 1, 1, 5, 4, 2, 6}

29 {0, 1, 1, 4, 9, 1, 2, 6, 1, 9, 2, 1, 4, 3, 3, 12, 1, 1, 8, 304, 1, 2, 2, 1, 1, 3, 1, 7, 4, 6}

29.53125 {0, 1, 1, 3, 3, 1, 5, 1, 1, 1, 2, 2, 13, 1, 45, 1, 13, 1, 1, 1, 1, 9, 1, 12, 2, 1, 1, 8, 1, 1}

30 {0, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2}

30.234375 {0, 1, 1, 2, 1, 1, 12, 1, 7, 21, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 5, 7, 4, 7, 1, 1, 2, 8, 2}

30.9375 {0, 1, 1, 2, 63, 1, 3, 1, 28, 3, 1, 5, 2, 1, 4, 13, 6, 2, 3, 13, 1, 6, 4, 1, 1, 1, 2, 3, 7, 2}

31 {0, 1, 1, 1, 1, 45, 1, 7, 4, 1, 3, 1, 72, 5, 65, 1, 1, 15, 2, 4, 5, 1, 3, 37, 1, 1, 9, 7, 1, 21}

31.640625 {0, 1, 1, 1, 1, 1, 1, 6, 1, 4, 6, 2, 4, 1, 2, 1, 7, 4, 1, 5, 1, 2, 16, 1, 1, 1, 11, 11, 1, 6}

32 {0, 1, 1, 1, 1, 1, 118, 1, 33, 1, 1, 2, 1, 1, 10, 6, 13, 1, 5, 3, 1, 2, 45, 6, 4, 6, 1, 3, 1, 9}

32.34375 {0, 1, 1, 1, 2, 1, 1, 1, 11, 1, 2, 47, 2, 3, 5, 1, 10, 10, 1, 3, 4, 2, 8, 47, 3, 2, 1, 23, 1, 3}

33 {0, 1, 1, 1, 5, 1, 3, 2, 1, 2, 2, 1, 3, 1, 10, 5, 1, 25, 1, 16, 1, 10, 3, 1, 4, 6, 2, 1, 1, 4}

33.046875 {0, 1, 1, 1, 6, 4, 4, 2, 3, 3, 4, 1, 3, 2, 1, 1, 1, 2, 2, 4, 1, 1, 5, 2, 2, 3, 1, 1, 11, 1}

33.75 {0, 1, 2, 73, 6, 2, 14, 4, 16, 3, 2, 3, 1, 2, 4, 1, 4, 1, 1, 1, 7, 1, 1, 2, 2, 1, 2, 2, 1, 5}

34 {0, 1, 2, 13, 1, 5, 11, 1, 3, 1, 1, 5, 3, 1, 4, 1, 1, 2, 6, 1, 1, 1, 1, 4, 6, 1, 1, 43, 1, 4}

34.453125 {0, 1, 2, 5, 2, 1, 1, 3, 1, 4, 1, 18, 1, 4, 1, 10, 75, 1, 2, 1, 1, 2, 4, 5, 1, 1, 1, 5, 1, 1}

35 {0, 1, 2, 2, 1, 47, 2, 15, 37, 1, 15, 1, 2, 1, 2, 200, 3, 8, 1, 1, 11, 1, 3, 1, 2, 2, 13, 8, 12, 2}

35.15625 {0, 1, 2, 2, 1, 1, 1, 1, 1, 3, 21, 1, 1, 15, 1, 5, 2, 2, 2, 6, 1, 1, 6, 2, 3, 1, 5, 1, 5, 3}

35.859375 {0, 1, 2, 1, 1, 1, 1, 4, 1, 2, 1, 4, 3, 13, 7, 5, 1, 2, 1, 1, 7, 1, 2, 3, 1, 24, 7, 1, 1, 2}

36 {0, 1, 2, 1, 1, 1, 10, 1, 2, 7, 22, 1, 51, 1, 1, 2, 7, 1, 9, 1, 1, 4, 2, 1, 12, 1, 7, 2, 4, 1}

36.5625 {0, 1, 2, 1, 6, 1, 2, 1, 3, 1, 1, 3, 3, 1, 1, 1, 1, 2, 5, 1, 3, 8, 2, 1, 16, 1, 1, 7, 116, 4}

37 {0, 1, 3, 17, 2, 1, 48, 1, 108, 2, 1, 3, 1, 1, 1, 5, 1, 2, 2, 12, 4, 4, 1, 9, 2, 1, 2, 4, 1, 1}

37.265625 {0, 1, 3, 5, 1, 1, 21, 1, 1, 7, 1, 1, 1, 3, 6, 2, 1, 1, 1, 5, 1, 7, 4, 3, 1, 5, 6, 11, 59, 1}

37.96875 {0, 1, 3, 1, 1, 4, 7, 4, 1, 12, 3, 1, 8, 1, 1, 2, 4, 1, 7, 5, 4, 2, 2, 1, 1, 1, 1, 1, 2, 1}

38 {0, 1, 3, 1, 1, 2, 1, 26, 1, 2, 3, 1, 92, 7, 4, 1, 6, 1, 1, 4, 18, 5, 5, 1, 1, 2, 1, 1, 1, 5}

38.671875 {0, 1, 4, 115, 1, 1, 2, 4, 7, 1, 5, 2, 2, 2, 1, 1, 1, 3, 18, 6, 2, 1, 1, 1, 1, 331, 6, 1, 2, 3}

39 {0, 1, 4, 3, 1, 7, 1, 19, 1, 5, 1, 1, 1, 1, 1, 18, 5, 7, 1, 1, 3, 2, 1, 2, 33, 1, 1, 11, 18, 7}

39.375 {0, 1, 4, 1, 1, 2, 1, 3, 4, 9, 5, 2, 2, 1, 3, 1, 2, 7, 3, 1, 14, 1, 1, 5, 1, 7, 1, 7, 4, 1}

40 {0, 1, 5, 4, 1, 1, 1, 6, 4, 27, 5, 5, 1, 1, 2, 1, 16, 4, 1, 2, 1, 1, 97, 3, 9, 2, 1, 3, 1, 1}

40.078125 {0, 1, 5, 3, 3, 1, 3, 5, 6, 1, 8, 1, 3, 4, 1, 4, 2, 1, 3, 1, 1, 1, 61, 1, 2, 1, 1, 1, 4, 8}

40.78125 {0, 1, 6, 3, 1, 1, 2, 5, 6, 1, 1, 209, 1, 4, 17, 1, 2, 1, 4, 34, 2, 10, 6, 2, 1, 2, 330, 1, 1, 1}

41 {0, 1, 6, 1, 1, 1, 6, 7, 2, 1, 4, 1, 1, 4, 10, 21, 1, 1, 1, 1, 2, 3, 1, 2, 1, 1, 1, 4, 49, 1}

41.484375 {0, 1, 7, 1, 1, 1, 3, 3, 1, 1, 2, 3, 10, 1, 1, 1, 10, 1, 21, 1, 13, 1, 1, 16, 1, 2, 5, 31, 8, 1}

42 {0, 1, 9, 24, 1, 1, 1, 5, 1, 9, 1, 1, 1, 2, 2, 17, 4, 1, 7, 1, 10, 2, 1, 1, 3, 3, 8, 2, 2, 1}

42.1875 {0, 1, 9, 1, 2, 9, 1, 2, 2, 2, 6, 2, 1, 2, 2, 2, 6, 1, 1, 3, 1, 4, 1, 3, 1, 6, 1, 2, 2, 1}

42.890625 {0, 1, 13, 13, 3, 6, 1, 1350, 1, 4, 8, 1, 2, 2, 2, 35, 1, 2, 2, 6, 6, 1, 1, 1, 17, 1, 3, 1, 1, 8}

43 {0, 1, 13, 1, 4, 2, 149, 3, 17, 1, 1, 1, 1, 2, 1, 3, 1, 18, 1, 7, 1, 8, 13, 12, 3, 14, 1, 2, 26, 4}

43.59375 {0, 1, 19, 1, 6, 1, 1, 3, 1, 1, 2, 18655, 2, 2, 12, 27, 4, 6, 1, 1, 2, 2, 142, 3, 2, 2, 3, 6, 6, 1}

44 {0, 1, 28, 6, 1, 8, 1, 3, 22, 1, 7, 2, 6, 4, 2, 2, 3, 1, 1, 1, 19, 5, 1, 1, 1, 3, 5, 2, 20, 4}

44.296875 {0, 1, 40, 4, 7, 4, 1, 4, 230, 2, 1, 1, 9, 1, 4, 3, 1, 2, 3, 47, 5, 1, 3, 1, 3, 1, 47, 1, 15, 1}