Idoneal numbers: Difference between revisions
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Added C# version, translated from python version, Added Pari/GP version from OEIS source |
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;* [[oeis:A000926|OEIS:A000926 - Euler's "numerus idoneus" (or "numeri idonei", or idoneal, or suitable, or convenient numbers)]] |
;* [[oeis:A000926|OEIS:A000926 - Euler's "numerus idoneus" (or "numeri idonei", or idoneal, or suitable, or convenient numbers)]] |
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=={{header|C#|CSharp}}== |
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{{trans|Python}} |
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<syntaxhighlight lang="csharp">using System; |
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class Program { |
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static void Main(string[] args) { |
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var sw = System.Diagnostics.Stopwatch.StartNew(); |
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int a, b, c, i, n, s3, ab; var res = new int[65]; |
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for (n = 1, i = 0; n < 1850; n++) { |
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bool found = true; |
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for (a = 1; a < n; a++) |
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for (b = a + 1, ab = a * b + a + b; b < n; b++, ab += a + 1) { |
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if (ab > n) break; |
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for (c = b + 1, s3 = ab + (b + a) * b; c < n; c++, s3 += b + a) { |
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if (s3 == n) found = false; |
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if (s3 >= n) break; |
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} |
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} |
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if (found) res[i++] = n; |
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} |
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sw.Stop(); |
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Console.WriteLine("The 65 known Idoneal numbers:"); |
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for (i = 0; i < res.Length; i++) |
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Console.Write("{0,5}{1}", res[i], i % 13 == 12 ? "\n" : ""); |
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Console.Write("Calculations took {0} ms", sw.Elapsed.TotalMilliseconds); |
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} |
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}</syntaxhighlight> |
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{{out}} |
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<pre>The 65 known Idoneal numbers: |
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1 2 3 4 5 6 7 8 9 10 12 13 15 |
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16 18 21 22 24 25 28 30 33 37 40 42 45 |
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48 57 58 60 70 72 78 85 88 93 102 105 112 |
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120 130 133 165 168 177 190 210 232 240 253 273 280 |
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312 330 345 357 385 408 462 520 760 840 1320 1365 1848 |
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Calculations took 28.5862 ms</pre> |
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=={{header|PARI/GP}}== |
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Adapted from the [[oeis:A000926|OEIS:A000926]] page. |
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<syntaxhighlight lang="parigp">ok(n) = !#select(k -> k <> 2, quadclassunit(-n << 2).cyc) \\ Andrew Howroyd, Jun 08 2018 |
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c = 0; for (n = 1, 1850, ok(n) & printf("%5d%s", n, if (c++ % 13 == 0, "\n", "")))</syntaxhighlight> |
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{{out}} |
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<pre> 1 2 3 4 5 6 7 8 9 10 12 13 15 |
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16 18 21 22 24 25 28 30 33 37 40 42 45 |
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48 57 58 60 70 72 78 85 88 93 102 105 112 |
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120 130 133 165 168 177 190 210 232 240 253 273 280 |
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312 330 345 357 385 408 462 520 760 840 1320 1365 1848</pre> |
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=={{header|Python}}== |
=={{header|Python}}== |
Revision as of 08:53, 24 September 2022
Idoneal numbers is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
Idoneal numbers (also called suitable numbers or convenient numbers) are the positive integers D such that any integer expressible in only one way as x2 ± Dy2 (where x2 is relatively prime to Dy2) is a prime power or twice a prime power.
A positive integer n is idoneal if and only if it cannot be written as ab + bc + ac for distinct positive integers a, b, and c with 0 < a < b < c.
There are only 65 known iodoneal numbers and is likely that no others exist. If there are others, it has been proven that there are at most, two more, and that no others exist below 1,000,000.
- Task
- Find and display at least the first 50 idoneal numbers (between 1 and 255).
- Stretch
- Find and display all 65 known idoneal numbers.
- See also
C#
using System;
class Program {
static void Main(string[] args) {
var sw = System.Diagnostics.Stopwatch.StartNew();
int a, b, c, i, n, s3, ab; var res = new int[65];
for (n = 1, i = 0; n < 1850; n++) {
bool found = true;
for (a = 1; a < n; a++)
for (b = a + 1, ab = a * b + a + b; b < n; b++, ab += a + 1) {
if (ab > n) break;
for (c = b + 1, s3 = ab + (b + a) * b; c < n; c++, s3 += b + a) {
if (s3 == n) found = false;
if (s3 >= n) break;
}
}
if (found) res[i++] = n;
}
sw.Stop();
Console.WriteLine("The 65 known Idoneal numbers:");
for (i = 0; i < res.Length; i++)
Console.Write("{0,5}{1}", res[i], i % 13 == 12 ? "\n" : "");
Console.Write("Calculations took {0} ms", sw.Elapsed.TotalMilliseconds);
}
}
- Output:
The 65 known Idoneal numbers: 1 2 3 4 5 6 7 8 9 10 12 13 15 16 18 21 22 24 25 28 30 33 37 40 42 45 48 57 58 60 70 72 78 85 88 93 102 105 112 120 130 133 165 168 177 190 210 232 240 253 273 280 312 330 345 357 385 408 462 520 760 840 1320 1365 1848 Calculations took 28.5862 ms
PARI/GP
Adapted from the OEIS:A000926 page.
ok(n) = !#select(k -> k <> 2, quadclassunit(-n << 2).cyc) \\ Andrew Howroyd, Jun 08 2018
c = 0; for (n = 1, 1850, ok(n) & printf("%5d%s", n, if (c++ % 13 == 0, "\n", "")))
- Output:
1 2 3 4 5 6 7 8 9 10 12 13 15 16 18 21 22 24 25 28 30 33 37 40 42 45 48 57 58 60 70 72 78 85 88 93 102 105 112 120 130 133 165 168 177 190 210 232 240 253 273 280 312 330 345 357 385 408 462 520 760 840 1320 1365 1848
Python
''' Rosetta code task: rosettacode.org/wiki/Idoneal_numbers '''
def is_idoneal(num):
''' Return true if num is an idoneal number '''
for a in range(1, num):
for b in range(a + 1, num):
if a * b + a + b > num:
break
for c in range(b + 1, num):
sum3 = a * b + b * c + a * c
if sum3 == num:
return False
if sum3 > num:
break
return True
row = 0
for n in range(1, 2000):
if is_idoneal(n):
row += 1
print(f'{n:5}', end='\n' if row % 13 == 0 else '')
- Output:
1 2 3 4 5 6 7 8 9 10 12 13 15 16 18 21 22 24 25 28 30 33 37 40 42 45 48 57 58 60 70 72 78 85 88 93 102 105 112 120 130 133 165 168 177 190 210 232 240 253 273 280 312 330 345 357 385 408 462 520 760 840 1320 1365 1848
Raku
First 60 in less than 1/2 second. The remaining 5 take another ~5 seconds.
sub is-idoneal ($n) {
my $idoneal = True;
I: for 1 .. $n -> $a {
for $a ^.. $n -> $b {
last if $a × $b + $a + $b > $n; # short circuit
for $b ^.. $n -> $c {
$idoneal = False and last I if (my $sum = $a × $b + $b × $c + $c × $a) == $n;
last if $sum > $n; # short circuit
}
}
}
$idoneal
}
$_».fmt("%4d").put for (1..1850).hyper(:32batch).grep( &is-idoneal ).batch(10)
- Output:
1 2 3 4 5 6 7 8 9 10 12 13 15 16 18 21 22 24 25 28 30 33 37 40 42 45 48 57 58 60 70 72 78 85 88 93 102 105 112 120 130 133 165 168 177 190 210 232 240 253 273 280 312 330 345 357 385 408 462 520 760 840 1320 1365 1848
Wren
import "./fmt" for Fmt
var isIdoneal = Fn.new { |n|
for (a in 1...n) {
for (b in a+1...n) {
if (a*b + a + b > n) break
for (c in b+1...n) {
var sum = a*b + b*c + a*c
if (sum == n) return false
if (sum > n) break
}
}
}
return true
}
var idoneals = []
for (n in 1..1850) if (isIdoneal.call(n)) idoneals.add(n)
Fmt.tprint("$4d", idoneals, 13)
- Output:
1 2 3 4 5 6 7 8 9 10 12 13 15 16 18 21 22 24 25 28 30 33 37 40 42 45 48 57 58 60 70 72 78 85 88 93 102 105 112 120 130 133 165 168 177 190 210 232 240 253 273 280 312 330 345 357 385 408 462 520 760 840 1320 1365 1848