Talk:Brazilian numbers: Difference between revisions
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(some observations hopefully to limit the need of tests) |
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:: I also noticed the difference two days ago, and I assumed that my REXX version was incorrect and was trying to find what the problem was in my computer program; I was hoping somebody else would calculate the 100,000<sup>th</sup> Brazilian number and verify it (or not). -- [[User:Gerard Schildberger|Gerard Schildberger]] ([[User talk:Gerard Schildberger|talk]]) 19:23, 14 August 2019 (UTC) |
:: I also noticed the difference two days ago, and I assumed that my REXX version was incorrect and was trying to find what the problem was in my computer program; I was hoping somebody else would calculate the 100,000<sup>th</sup> Brazilian number and verify it (or not). -- [[User:Gerard Schildberger|Gerard Schildberger]] ([[User talk:Gerard Schildberger|talk]]) 19:23, 14 August 2019 (UTC) |
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==some observations not proofs == |
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I tried to check the maximal base needed for an odd brazilian number.<BR> |
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If a number is brazilian the maximal base to test is always less equal number / 3.<BR> |
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If a number is prime and brazilian then the maximal base is square root of number.<BR> |
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[https://tio.run/##lVRNb@IwEL3nV8yhhxhBl9JDV9BWKiSokdgEbehqV4iDSRwwGxzkmFZt1b@@rO04H/Rjq72AM29m3vjNeHY4j3DaSXbR4bDj2YrjLSw5fqIpxczfb5eE5wPr@cQbO@4YxtPRiwXwfPItcFxw3Mn01nuRqDsJ3QK4mU5nv6YujAI/DCauBn3HG79YUcZyIX3ge3DnOyFcwVm32x0oSzgJZiN/pky9gXWPuTSOsj0TYZqJHPqAOceP8@7pqfHsnC0gS@COMnHeUylovuN0S5quBU1LkmjfZZalBLOBZclrRiTecwIeo2Kq4kpS2t70wceC3hOVe2AtyYoyCSQ0TaM15rYhmvcW7ZA@kSyRFp0CdXrtaM3tgMe24HuCENKFQf8KdIkPa5oSoC0Kl1dwS1frKhLiTOJDQwXgjcFAc7oAsSaFuXbYqKQykxbPJN58kLYZV@k03yxUigSnORmUEIvsTZui4puw@NVB4QWqTfrHspI9iwTNGIzWJPp9k6Yh3hKHrqjIbabHp73EOWmqivpVLwrVOclFO1Yx8L760mGfiqOKVYwyFBzgeD9A8SjIZKqwjkZaKqLug46/hu5r7U2MjC79/8mlm2W/JUJweW0KqfoH4P70ZpWAzWupgSklrRT18mH5EA1D34jjKRGHxyIq6ko@T6k3/Fg9WbSp@RIu6grL@l4XpgP8TNhBHNvFUkDobViScVOGHHkQmeHo9MpJpMknY4Lem3YdVw5u4bxoqqqeAKeCpJVMZ91i6Mx/y3ygctTrJsv7ybFW@JfC2DIbBjWfRb2LSv4KLu/@TlON2kVXy/3C6hE/alJjFQGMpZB6cUyyhwY5UprqJ960GW0bNVL9uOVqLfeP3rJMnS7qF8A@30PJ8Qyipur1OijOrN1D9WiXDTnKj5pIEatuyv7zpjrDUU8W/a9IC316OPyJkhSv8kMnOP8L Try it online!] |
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<pre>// only primes are shown |
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number base base*base |
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13 3 9 |
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31 2 4 |
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43 6 36 |
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73 8 64 |
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127 2 4 |
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157 12 144 |
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211 14 196 |
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241 15 225 |
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307 17 289 |
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421 20 400 |
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463 21 441 |
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601 24 576 |
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757 27 729 |
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1093 3 9 |
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1123 33 1089 |
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1483 38 1444 |
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.. |
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55987 6 36 |
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60271 245 60025 |
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60763 246 60516 |
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71023 266 70756 |
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74257 272 73984 |
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77563 278 77284 |
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78121 279 77841 |
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82657 287 82369 |
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83233 288 82944 |
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84391 290 84100 |
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86143 293 85849 |
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88741 17 289 |
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95791 309 95481 |
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98911 314 98596 |
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odd brazilian numbers 7 .. 100000 : 40428 |
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slots: base/number |
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<=1/12 <= 2/12 <=3/12 <=4/12 |
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30717 4013 2225 3473 0 0 0 0 0 0 0 0<pre> |
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Revision as of 07:20, 15 August 2019
wee discrepancy
Is it possible to be a little more specific regarding the "wee discrepancy" with the F# version? <lang fsharp> printfn "%d" (Seq.item 3999 (Brazilian())) </lang> prints 4618--Nigel Galloway (talk) 17:05, 14 August 2019 (UTC)
- OK I think I've found it--Nigel Galloway (talk) 17:37, 14 August 2019 (UTC)
- I also noticed the difference two days ago, and I assumed that my REXX version was incorrect and was trying to find what the problem was in my computer program; I was hoping somebody else would calculate the 100,000th Brazilian number and verify it (or not). -- Gerard Schildberger (talk) 19:23, 14 August 2019 (UTC)
some observations not proofs
I tried to check the maximal base needed for an odd brazilian number.
If a number is brazilian the maximal base to test is always less equal number / 3.
If a number is prime and brazilian then the maximal base is square root of number.
Try it online!
// only primes are shown
number base base*base
13 3 9
31 2 4
43 6 36
73 8 64
127 2 4
157 12 144
211 14 196
241 15 225
307 17 289
421 20 400
463 21 441
601 24 576
757 27 729
1093 3 9
1123 33 1089
1483 38 1444
..
55987 6 36
60271 245 60025
60763 246 60516
71023 266 70756
74257 272 73984
77563 278 77284
78121 279 77841
82657 287 82369
83233 288 82944
84391 290 84100
86143 293 85849
88741 17 289
95791 309 95481
98911 314 98596
odd brazilian numbers 7 .. 100000 : 40428
slots: base/number
<=1/12 <= 2/12 <=3/12 <=4/12
30717 4013 2225 3473 0 0 0 0 0 0 0 0