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Nachkommastellengleichverteilungspositionen
(Decimal places uniform distribution positions from irrational numbers) |
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Beispiel: |
10 Ziffern von Pi ab Position 60: |
4592307816 |
ist jede Ziffer genau 1 mal vertreten (exakt
gleichverteilt: Chi²=0) |
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oeis.org -> |
A000796 |
A001113 |
A002193 |
A013663 |
A133731 |
A060196 |
A001622 |
A002162 |
Bereichsgröße |
Position mit Chi²=0 bei Pi |
Position mit Chi²=0 bei e |
Position mit Chi²=0 bei √2 |
Zeta[5] |
Ziegenfaktor |
√(e*Pi/2)*erf(1/√2) |
(1 + √5)/2 |
ln(2) |
10 |
60 |
1729 |
272 |
996 |
9646 |
3726 |
3042 |
226 |
20 |
33673 |
35692 |
115604 |
15949 |
31791 |
31284 |
40 |
77071 |
30 |
101390 |
16975 |
1041002 |
42218 |
275084 |
321678 |
961522 |
114140 |
40 |
142620 |
148521 |
29208 |
888757 |
735884 |
1768331 |
17360 |
518604 |
50 |
145870 |
5255889 |
2553689 |
2400782 |
6737937 |
53536 |
355072 |
205796 |
60 |
4008553 |
4058846 |
9554667 |
2634556 |
2871866 |
14996797 |
1736320 |
772897 |
70 |
11937122 |
214212 |
4611964 |
244014 |
798117 |
6139237 |
6039842 |
2745330 |
80 |
5615264 |
1286123 |
6406211 |
1217569 |
1975152 |
46238329 |
8816333 |
72931576 |
90 |
16960375 |
58609097 |
7843131 |
13465487 |
23180013 |
4448207 |
224877 |
27859095 |
100 |
43823961 |
96158000 |
17102940 |
62347336 |
43519119 |
48901790 |
13950453 |
41210764 |
110 |
129525713 |
11306008 |
10366693 |
23111019 |
483700 |
7537493 |
96479940 |
17003040 |
120 |
111980338 |
100583378 |
176673017 |
53649903 |
77797113 |
58143324 |
7680396 |
62225241 |
130 |
111980334 |
41724593 |
12877057 |
274194364 |
32814146 |
52865862 |
481754806 |
8176635 |
140 |
199567417 |
482553820 |
133345052 |
156350736 |
29787938 |
435652381 |
227792358 |
487011365 |
150 |
496766605 |
358575538 |
674992212 |
92879196 |
579103756 |
33976908 |
19279826 |
318932166 |
160 |
1294588 |
43988059 |
145088529 |
270038857 |
906095304 |
657451218 |
172560512 |
456371475 |
170 |
189136635 |
1302228192 |
121122536 |
293273678 |
362963848 |
279164660 |
392481116 |
44859022 |
180 |
377226241 |
1060431551 |
78377358 |
> 500 Mio. |
> 1,1 Mrd |
> 1,1 Mrd |
266253045 |
307765742 |
190 |
74359665 |
1383909731 |
415171588 |
158831424 |
> 1,1 Mrd |
8842877 |
100954703 |
228446473 |
200 |
722098989 |
1749546327 |
428790895 |
> 500 Mio. |
597784458 |
799440195 |
> 1 Mrd. |
> 1 Mrd. |
300 |
18215426129 |
1358348133 |
190184264 |
> 500 Mio. |
> 1,1 Mrd |
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400 |
11217740553 |
> 4 Mrd |
> 1 Mrd. |
> 500 Mio. |
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500 |
3723677022 |
> 4 Mrd |
> 1 Mrd. |
> 500 Mio. |
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600 |
8679204764 |
2381329141 |
> 1 Mrd. |
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660 |
62040518510 |
> 4 Mrd |
> 1 Mrd. |
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670 |
70737212276 |
> 4 Mrd |
> 1 Mrd. |
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680 |
73671827913 |
> 4 Mrd |
> 1 Mrd. |
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690 |
56098573234 |
> 4 Mrd |
> 1 Mrd. |
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700 |
318525142276 |
> 4 Mrd |
> 1 Mrd. |
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800 |
702835521712 |
> 4 Mrd |
> 1 Mrd. |
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900 |
>10^12 |
> 4 Mrd |
> 1 Mrd. |
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1000 |
895698980824 |
> 4 Mrd |
> 1 Mrd. |
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1010 |
>199 Mrd |
> 4 Mrd |
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1020 |
>199 Mrd |
> 4 Mrd |
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1100 |
>99 Mrd |
> 4 Mrd |
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1200 |
889299854723 |
> 4 Mrd |
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1280 |
>99 Mrd |
> 4 Mrd |
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2000 |
3281800467620 |
> 4 Mrd |
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Zahlenfolgen als Array: |
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Position bei Pi: |
60,33673,101390,142620,145870,4008553,11937122,5615264,16960375,43823961,129525713,111980338,111980334,199567417,496766605,… |
Position bei e: |
1729,35692,16975,148521,5255889,4058846,214212,1286123,58609097,96158000,11306008,100583378,41724593,482553820,358575538,… |
Position bei √2: |
272,115604,1041002,29208,2553689,9554667,4611964,6406211,7843131,17102940,10366693,176673017,12877057,133345052,674992212,… |
Zeta[5]: |
996,15949,42218,888757,2400782,2634556,244014,1217569,13465487,62347336,23111019,53649903,274194364,156350736,92879196,… |
A133731: |
9646,31791,275084,735884,6737937,2871866,798117,1975152,23180013,43519119,483700,77797113,32814146,29787938,579103756,… |
A060196: |
3726,31284,321678,1768331,53536,14996797,6139237,46238329,4448207,48901790,7537493,58143324,52865862,435652381,33976908,… |
A001622: |
3042,40,961522,17360,355072,1736320,6039842,8816333,224877,13950453,96479940,7680396,481754806,227792358,19279826,… |
A002162=ln(2): |
226,77071,114140,518604,205796,772897,2745330,72931576,27859095,41210764,17003040,62225241,8176635,487011365,318932166,… |
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11.05.2024 |
gerd (at) gerdlamprecht . de |
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