Idoneal numbers: Difference between revisions
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{{
'''[[wp:Idoneal_number|Idoneal numbers]]''' (also called '''suitable''' numbers or '''convenient''' numbers) are the positive integers '''D''' such that any integer expressible in only one way as '''x<sup>2</sup> ± Dy<sup>2</sup>''' (where '''x<sup>2</sup>''' is relatively prime to '''Dy<sup>2</sup>''') is a prime power or twice a prime power.
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</syntaxhighlight>
{{out}}
<pre>
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
</pre>
=={{header|ABC}}==
<syntaxhighlight lang="abc">
HOW TO RETURN a over b: RETURN floor( a / b )
HOW TO REPORT is.idoneal n:
PUT 1 IN idoneal
PUT 0 IN a
PUT n over 2 IN max.a
WHILE idoneal = 1 AND a < max.a:
PUT a + 1 IN a
PUT a IN b
PUT n IN c
PUT 0 IN sum
PUT 1 IN again
WHILE b < c AND b < n - 1 AND sum <= n AND idoneal = 1:
PUT b + 1 IN b
PUT a * b IN ab
PUT ( n - ab ) over ( a + b ) IN c
PUT ab + ( c * ( b + a ) ) IN sum
IF c > b AND sum = n:
PUT 0 IN idoneal
REPORT idoneal = 1
PUT 0 IN count
PUT 0 IN n
WHILE count < 65:
PUT n + 1 IN n
IF is.idoneal n:
WRITE n >> 5
PUT count + 1 IN count
IF count mod 13 = 0: WRITE /
</syntaxhighlight>
{{out}}
<pre>
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FOR n WHILE count < max count DO
BOOL idoneal := TRUE;
FOR a TO n
FOR b FROM a + 1 TO n - 1
WHILE INT ab = a * b;
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INT sum = ab + ( c * ( b + a ) );
sum <= n
AND b < c
AND ( idoneal := c <= b OR sum /= n )
DO SKIP OD
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OD
END
</syntaxhighlight>
{{out}}
<pre>
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
</pre>
=={{header|ALGOL W}}==
<syntaxhighlight lang="algolw">
begin % find idoneal numbers - numbers that cannot be written as ab + bc + ac %
% where 0 < a < b < c %
% there are 65 known idoneal numbers %
integer count, MAX_COUNT, n;
MAX_COUNT := 65;
count := 0;
n := 0;
while count < MAX_COUNT do begin
logical idoneal;
integer a;
n := n + 1;
idoneal := true;
a := 1;
while ( a + 2 ) < n and idoneal do begin
integer b;
b := a + 1;
while begin
integer ab, sum;
ab := a * b;
sum := 0;
if ab < n then begin
integer c;
c := ( n - ab ) div ( a + b );
sum := ab + ( c * ( b + a ) );
if c > b and sum = n then idoneal := false;
b := b + 1
end if_ab_lt_n ;
sum <= n and idoneal and ab < n
end do begin end;
a := a + 1
end;
if idoneal then begin
count := count + 1;
writeon( i_w := 4, s_w := 0, " ", n );
if count rem 13 = 0 then write()
end if_idoneal
end while_count_lt_MAX_COUNT
end.
</syntaxhighlight>
{{out}}
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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</pre>
=={{header|EasyLang}}==
{{trans|Lua}}
<syntaxhighlight lang=easylang>
maxCount = 65
while count < maxCount
n += 1
idoneal = 1
a = 1
while a + 2 < n and idoneal = 1
b = a + 1
repeat
ab = a * b
sum = 0
if ab < n
c = (n - ab) div (a + b)
sum = ab + c * (b + a)
if c > b and sum = n
idoneal = 0
.
b += 1
.
until sum > n or idoneal = 0 or ab >= n
.
a += 1
.
if idoneal = 1
count += 1
write " " & n
.
.
</syntaxhighlight>
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312 330 345 357 385 408 462 520 760 840 1320 1365 1848
</pre>
=={{header|Go}}==
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b = b + 1
end
until sum > n or not idoneal
a = a + 1
end
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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
</pre>
=={{header|MiniScript}}==
<syntaxhighlight lang="miniscript">
isIdoneal = function(n)
for a in range(1, n)
for b in range(a + 1, n)
if a * b + a + b > n then break
for c in range(b + 1, n)
sum3 = a * b + b * c + a * c
if sum3 == n then return false
if sum3 > n then break
end for
end for
end for
return true
end function
idoneals = []
for n in range(1, 2000)
if isIdoneal(n) then idoneals.push(n)
end for
print idoneals.join(", ")
</syntaxhighlight>
{{out}}
<pre>
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
</pre>
Line 1,026 ⟶ 1,179:
1365
1848
</pre>
=={{header|PL/M}}==
{{works with|8080 PL/M Compiler}} ... under CP/M (or an emulator)
<syntaxhighlight lang="plm">
100H: /* FIND IDONEAL NUMBERS - NUMBERS THAT CANNOT BE WRITTEN */
/* AS AB + BC + AC WHERE 0 < A < B < C */
/* THERE ARE 65 KNOWN IDONEAL NUMBERS */
/* CP/M BDOS SYSTEM CALL AND I/O ROUTINES */
BDOS: PROCEDURE( FN, ARG ); DECLARE FN BYTE, ARG ADDRESS; GOTO 5; END;
PR$CHAR: PROCEDURE( C ); DECLARE C BYTE; CALL BDOS( 2, C ); END;
PR$STRING: PROCEDURE( S ); DECLARE S ADDRESS; CALL BDOS( 9, S ); END;
PR$NL: PROCEDURE; CALL PR$CHAR( 0DH ); CALL PR$CHAR( 0AH ); END;
PR$NUMBER: PROCEDURE( N ); /* PRINTS A NUMBER IN THE MINIMUN FIELD WIDTH */
DECLARE N ADDRESS;
DECLARE V ADDRESS, N$STR ( 6 )BYTE, W BYTE;
V = N;
W = LAST( N$STR );
N$STR( W ) = '$';
N$STR( W := W - 1 ) = '0' + ( V MOD 10 );
DO WHILE( ( V := V / 10 ) > 0 );
N$STR( W := W - 1 ) = '0' + ( V MOD 10 );
END;
CALL PR$STRING( .N$STR( W ) );
END PR$NUMBER;
/* TASK */
DECLARE TRUE LITERALLY '0FFH', FALSE LITERALLY '0';
DECLARE ( COUNT, N, A, B, C, AB, SUM ) ADDRESS;
DECLARE ( IDONEAL, FINISHED ) BYTE;
DECLARE MAX$COUNT LITERALLY '65';
COUNT, N = 0;
DO WHILE COUNT < MAX$COUNT;
N = N + 1;
IDONEAL = TRUE;
A = 1;
DO WHILE ( A + 2 ) < N AND IDONEAL;
B = A + 1;
FINISHED = FALSE;
DO WHILE NOT FINISHED;
AB = A * B;
SUM = 0;
IF AB < N THEN DO;
C = ( N - AB ) / ( A + B );
SUM = AB + ( C * ( B + A ) );
IF C > B AND SUM = N THEN IDONEAL = FALSE;
B = B + 1;
END;
FINISHED = SUM > N OR NOT IDONEAL OR AB >= N;
END;
A = A + 1;
END;
IF IDONEAL THEN DO;
CALL PR$CHAR( ' ' );
IF N < 10 THEN CALL PR$CHAR( ' ' );
IF N < 100 THEN CALL PR$CHAR( ' ' );
IF N < 1000 THEN CALL PR$CHAR( ' ' );
CALL PR$NUMBER( N );
IF ( COUNT := COUNT + 1 ) MOD 13 = 0 THEN CALL PR$NL;
END;
END;
EOF
</syntaxhighlight>
{{out}}
<pre>
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
</pre>
Line 1,186 ⟶ 1,413:
{{trans|Raku}}
{{libheader|Wren-fmt}}
<syntaxhighlight lang="
var isIdoneal = Fn.new { |n|
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