Rhonda numbers: Difference between revisions
Added Algol 68
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=={{header|ALGOL 68}}==
<syntaxhighlight lang="algol68">
BEGIN # find some Rhonda numbers: numbers n in base b such that the product #
# of the digits of n is b * the sum of the prime factors of n #
# returns the sum of the prime factors of n #
PROC factor sum = ( INT n )INT:
BEGIN
INT result := 0;
INT v := ABS n;
WHILE v > 1 AND v MOD 2 = 0 DO
result +:= 2;
v OVERAB 2
OD;
FOR f FROM 3 BY 2 WHILE v > 1 DO
WHILE v > 1 AND v MOD f = 0 DO
result +:= f;
v OVERAB f
OD
OD;
result
END # factor sum # ;
# returns the digit product of n in the specified base #
PROC digit product = ( INT n, base )INT:
IF n = 0 THEN 0
ELSE
INT result := 1;
INT v := ABS n;
WHILE v > 0 DO
result *:= v MOD base;
v OVERAB base
OD;
result
FI # digit product # ;
# returns TRUE if n is a Rhonda number in the specified base, #
# FALSE otherwise #
PROC is rhonda = ( INT n, base )BOOL: base * factor sum( n ) = digit product( n, base );
# returns TRUE if n is prime, FALSE otherwise #
PROC is prime = ( INT n )BOOL:
IF n < 3 THEN n = 2
ELIF n MOD 3 = 0 THEN n = 3
ELIF NOT ODD n THEN FALSE
ELSE
INT f := 5;
INT f2 := 25;
INT to next := 24;
BOOL is a prime := TRUE;
WHILE f2 <= n AND is a prime DO
is a prime := n MOD f /= 0;
f +:= 2;
f2 +:= to next;
to next +:= 8
OD;
is a prime
FI # is prime # ;
# returns a string representation of n in the specified base #
PROC to base string = ( INT n, base )STRING:
IF n = 0 THEN "0"
ELSE
INT under 10 = ABS "0";
INT over 9 = ABS "a" - 10;
STRING result := "";
INT v := ABS n;
WHILE v > 0 DO
INT d = v MOD base;
REPR ( d + IF d < 10 THEN under 10 ELSE over 9 FI ) +=: result;
v OVERAB base
OD;
result
FI # to base string # ;
# find the first few Rhonda numbers in non-prime bases 2 .. max base #
INT max rhonda = 10;
INT max base = 16;
FOR base FROM 2 TO max base DO
IF NOT is prime( base ) THEN
print( ( "The first ", whole( max rhonda, 0 )
, " Rhonda numbers in base ", whole( base, 0 )
, ":", newline
)
);
INT r count := 0;
[ 1 : max rhonda ]INT rhonda;
FOR n WHILE r count < max rhonda DO
IF is rhonda( n, base ) THEN
rhonda[ r count +:= 1 ] := n
FI
OD;
print( ( " in base 10:" ) );
FOR i TO max rhonda DO print( ( " ", whole( rhonda[ i ], 0 ) ) ) OD;
print( ( newline ) );
IF base /= 10 THEN
print( ( " in base ", whole( base, -2 ), ":" ) );
FOR i TO max rhonda DO print( ( " ", to base string( rhonda[ i ], base ) ) ) OD;
print( ( newline ) )
FI
FI
OD
END
</syntaxhighlight>
{{out}}
<pre>
The first 10 Rhonda numbers in base 4:
in base 10: 10206 11935 12150 16031 45030 94185 113022 114415 191149 244713
in base 4: 2133132 2322133 2331312 3322133 22333212 112333221 123211332 123323233 232222231 323233221
The first 10 Rhonda numbers in base 6:
in base 10: 855 1029 3813 5577 7040 7304 15104 19136 35350 36992
in base 6: 3543 4433 25353 41453 52332 53452 153532 224332 431354 443132
The first 10 Rhonda numbers in base 8:
in base 10: 1836 6318 6622 10530 14500 14739 17655 18550 25398 25956
in base 8: 3454 14256 14736 24442 34244 34623 42367 44166 61466 62544
The first 10 Rhonda numbers in base 9:
in base 10: 15540 21054 25331 44360 44660 44733 47652 50560 54944 76857
in base 9: 23276 31783 37665 66758 67232 67323 72326 76317 83328 126376
The first 10 Rhonda numbers in base 10:
in base 10: 1568 2835 4752 5265 5439 5664 5824 5832 8526 12985
The first 10 Rhonda numbers in base 12:
in base 10: 560 800 3993 4425 4602 4888 7315 8296 9315 11849
in base 12: 3a8 568 2389 2689 27b6 29b4 4297 4974 5483 6a35
The first 10 Rhonda numbers in base 14:
in base 10: 11475 18655 20565 29631 31725 45387 58404 58667 59950 63945
in base 14: 4279 6b27 76cd ab27 b7c1 1277d 173da 17547 17bc2 19437
The first 10 Rhonda numbers in base 15:
in base 10: 2392 2472 11468 15873 17424 18126 19152 20079 24388 30758
in base 15: a97 aec 35e8 4a83 5269 5586 5a1c 5e39 735d 91a8
The first 10 Rhonda numbers in base 16:
in base 10: 1000 1134 6776 15912 19624 20043 20355 23946 26296 29070
in base 16: 3e8 46e 1a78 3e28 4ca8 4e4b 4f83 5d8a 66b8 718e
</pre>
=={{header|Arturo}}==
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