Talk:First perfect square in base n with n unique digits: Difference between revisions
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(Finding maximal distances to check if number needs extra digit) |
m (→Finding maximal distances to check if number needs extra digit: how to find the values with formula) |
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I checked all solutions for the possibly inserted digits.This makes only sense, if the inserted digit ist "small" , so that one will find a solution, before this inserted digit is reached by sqr(num) |
I checked all solutions for the possibly inserted digits.This makes only sense, if the inserted digit ist "small" , so that one will find a solution, before this inserted digit is reached by sqr(num) |
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<pre> |
<pre> |
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Base 17 -> base-1 = 16 |
Base 17 -> base-1 = 16 -> (base-1) / 2 = 8 |
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insert 1 this is the relevant digit -> smallest startvalue. |
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insert 1 |
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dgt/count: digital roots of 3,5,11,13 lead to possible solution |
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1 4 : 3 5 11 13 //distances = +2 = diff1 =(8-2*k) +6= (8-diff1) |
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0+3,8-3,8+3,16-3, 16+3,24-3, n*((Base-1)/2) +/- k (= first found value ) k = 3 |
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8 4 : 4 8 12 16 //distances = +4 +4 +4 +4 |
8 4 : 4 8 12 16 //distances = +4 +4 +4 +4 |
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0+4,8-4,8+4,16-4, 16+4,24-4, |
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9 4 : 1 7 9 15 //distances = +6 +2 +6 +2 |
9 4 : 1 7 9 15 //distances = +6 +2 +6 +2 |
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0+1,8-1,8+1,16-1, 16+1,24-1, |
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Base 21 -> base-1 = 20 |
Base 21 -> base-1 = 20 -> 10 |
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insert 6 |
insert 6 |
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6 4 : 4 6 14 16 // +2 +8 +2 +8 |
6 4 : 4 6 14 16 // +2 +8 +2 +8 |
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Ed: 0+4,10-4,10+4,20-4, 20+4... |
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⚫ | |||
11 4 : 1 9 11 19 // +8 +2 +8 +2 |
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14 4 : 2 8 12 18 // +6 +4 +6 +4 |
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15 2 : 5 15 // +10 +10 |
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19 4 : 3 7 13 17 // +6 +6 +4 +4 |
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⚫ | |||
insert 2 |
insert 2 |
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2 4 : 4 10 18 24 // +6 +8 +6 +8 |
2 4 : 4 10 18 24 // +6 +8 +6 +8 |
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0+4,14-4,14+4,28-4, 28+4 |
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11 4 : 5 9 19 23 //+4 +10 +4 10 |
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14 2 : 14 28 //+14 +14 |
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15 4 : 1 13 15 27 //+12+2+12+2 |
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18 4 : 2 12 16 26 //+10+4+10+4 |
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22 4 : 6 8 20 22 //+2+12+2+12 |
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23 4 : 3 11 17 25 //+8+6+8+6 |
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</pre> |
</pre> |
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Now one sees that only few different distances need to be calculated.In the case of base 29 only 4 out of 28 = 1/7 => runtime about 700 s.Or for a 4-core CPU test every 28 from the different start values. |
Now one sees that only few different distances need to be calculated.In the case of base 29 only 4 out of 28 = 1/7 => runtime about 700 s.Or for a 4-core CPU test every 28 from the different start values. |
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For base 49 one needs 8 Core to check every 48 ;-) |
For base 49 one needs 8 Core to check every 48 ;-) |
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<pre> Base 49 |
<pre> Base 49 48-> 24 ->12 -> 6 ( 5+1 = 6 ? ) |
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insert 1 |
insert 1 |
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1 8 : 5 11 13 19 29 35 37 43 //+6+2+6+10+6+2+6+10</pre> |
1 8 : 5 11 13 19 29 35 37 43 //+6+2+6+10+6+2+6+10</pre> |
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0+5,12-1(= 6-5),12+1,24-5,24+5,36-1,36+1,48-5 |