Brazilian numbers: Difference between revisions
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First 20 prime brazilian numbers:
7 13 31 43 73 127 157 211 241 307 421 463 601 757 1093 1123 1483 1723 2551 2801</pre>
=={{header|AWK}}==
<syntaxhighlight lang="awk">
Line 511 ⟶ 512:
first 20 prime Brazilian numbers: 7 13 31 43 73 127 157 211 241 307 421 463 601 757 1093 1123 1483 1723 2551 2801
</pre>
=={{header|BASIC}}==
==={{header|ANSI BASIC}}===
{{trans|Modula-2}}
{{works with|Decimal BASIC}}
<syntaxhighlight lang="basic">
1000 REM Brazilian numbers
1010 DECLARE EXTERNAL FUNCTION IsBrazilian
1020 DECLARE EXTERNAL FUNCTION SameDigits
1030 DECLARE EXTERNAL FUNCTION IsPrime
1040 PRINT "First 20 Brazilian numbers:"
1050 LET C = 0
1060 LET N = 7
1070 DO WHILE C < 20
1080 IF IsBrazilian(N) <> 0 THEN
1090 PRINT N;
1100 LET C = C + 1
1110 END IF
1120 LET N = N + 1
1130 LOOP
1140 PRINT
1150 PRINT
1160 PRINT "First 20 odd Brazilian numbers:"
1170 LET C = 0
1180 LET N = 7
1190 DO WHILE C < 20
1200 IF IsBrazilian(N) <> 0 THEN
1210 PRINT N;
1220 LET C = C + 1
1230 END IF
1240 LET N = N + 2
1250 LOOP
1260 PRINT
1270 PRINT
1280 PRINT "First 20 prime Brazilian numbers:"
1290 LET C = 0
1300 LET N = 7
1310 DO WHILE C < 20
1320 IF IsBrazilian(N) <> 0 THEN
1330 PRINT N;
1340 LET C = C + 1
1350 END IF
1360 DO
1370 LET N = N + 2
1380 LOOP WHILE IsPrime(N) = 0
1390 LOOP
1400 PRINT
1410 END
1420 REM
1430 EXTERNAL FUNCTION IsBrazilian(N)
1440 REM Result: 1 if N is Brazilian, 0 otherwise
1450 IF N < 7 THEN
1460 LET IsBrazilian = 0
1470 ELSEIF (MOD(N, 2) = 0) AND (N >= 8) THEN
1480 LET IsBrazilian = 1
1490 ELSE
1500 FOR B = 2 TO N - 2
1510 IF SameDigits(N, B) <> 0 THEN
1520 LET IsBrazilian = 1
1530 EXIT FUNCTION
1540 END IF
1550 NEXT B
1560 LET IsBrazilian = 0
1570 END IF
1580 END FUNCTION
1590 REM
1600 EXTERNAL FUNCTION SameDigits(N, B)
1610 REM Result: 1 if N has same digits in the base B, 0 otherwise
1620 LET NL = N ! Local N
1630 LET F = MOD(NL, B)
1640 LET NL = INT(NL / B)
1650 DO WHILE NL > 0
1660 IF MOD(NL, B) <> F THEN
1670 LET SameDigits = 0
1680 EXIT FUNCTION
1690 END IF
1700 LET NL = INT(NL / B)
1710 LOOP
1720 LET SameDigits = 1
1730 END FUNCTION
1740 REM
1750 EXTERNAL FUNCTION IsPrime(N)
1760 REM Result: non-zero if N is prime, 0 otherwise
1770 IF N < 2 THEN
1780 LET IsPrime = 0
1790 ELSEIF MOD(N, 2) = 0 THEN
1800 REM IsPrime = (N = 2)
1810 IF N = 2 THEN
1820 LET IsPrime = 1
1830 ELSE
1840 LET IsPrime = 0
1850 END IF
1860 ELSEIF MOD(N, 3) = 0 THEN
1870 REM IsPrime = (N = 3)
1880 IF N = 3 THEN
1890 LET IsPrime = 1
1900 ELSE
1910 LET IsPrime = 0
1920 END IF
1930 ELSE
1940 LET D = 5
1950 DO WHILE D * D <= N
1960 IF MOD(N, D) = 0 THEN
1970 LET IsPrime = 0
1980 EXIT FUNCTION
1990 ELSE
2000 LET D = D + 2
2010 IF MOD(N, D) = 0 THEN
2020 LET IsPrime = 0
2030 EXIT FUNCTION
2040 ELSE
2050 LET D = D + 4
2060 END IF
2070 END IF
2080 LOOP
2090 LET IsPrime = 1
2100 END IF
2110 END FUNCTION
</syntaxhighlight>
{{out}}
<pre>
First 20 Brazilian numbers:
7 8 10 12 13 14 15 16 18 20 21 22 24 26 27 28 30 31 32 33
First 20 odd Brazilian numbers:
7 13 15 21 27 31 33 35 39 43 45 51 55 57 63 65 69 73 75 77
First 20 prime Brazilian numbers:
7 13 31 43 73 127 157 211 241 307 421 463 601 757 1093 1123 1483 1723 2551 2801
</pre>
==={{header|FreeBASIC}}===
{{trans|Visual Basic .NET}}
<syntaxhighlight lang="freebasic">Function sameDigits(Byval n As Integer, Byval b As Integer) As Boolean
Dim f As Integer = n Mod b : n \= b
While n > 0
If n Mod b <> f Then Return False Else n \= b
Wend
Return True
End Function
Function isBrazilian(Byval n As Integer) As Boolean
If n < 7 Then Return False
If n Mod 2 = 0 Then Return True
For b As Integer = 2 To n - 2
If sameDigits(n, b) Then Return True
Next b
Return False
End Function
Function isPrime(Byval n As Integer) As Boolean
If n < 2 Then Return False
If n Mod 2 = 0 Then Return n = 2
If n Mod 3 = 0 Then Return n = 3
Dim d As Integer = 5
While d * d <= n
If n Mod d = 0 Then Return False Else d += 2
If n Mod d = 0 Then Return False Else d += 4
Wend
Return True
End Function
Dim kind(2) As String ={"", "odd", "prime"}
For i As Integer = 0 To 2
Print Using "First 20 & Brazilian numbers: "; kind(i)
Dim Limit As Integer = 20, n As Integer = 7
Do
If isBrazilian(n) Then Print Using "& "; n; : Limit -= 1
Select Case kind(i)
Case "" : n += 1
Case "odd" : n += 2
Case "prime" : Do : n += 2 : Loop Until isPrime(n)
End Select
Loop While Limit > 0
Next i
Sleep</syntaxhighlight>
==={{header|Nascom BASIC}}===
{{trans|Modula-2}}
{{works with|Nascom ROM BASIC|4.7}}
This version shows only the first 12 prime Brazilian numbers because of slow work.
<syntaxhighlight lang="basic">
10 REM Brazilian numbers
20 PRINT "First 20 Brazilian numbers:"
30 C=0:N=7
40 IF C>=20 THEN 90
50 GOSUB 320
60 IF BR THEN PRINT N;:C=C+1
70 N=N+1
80 GOTO 40
90 PRINT:PRINT
100 PRINT "First 20 odd Brazilian numbers:"
110 C=0:N=7
120 IF C>=20 THEN 170
130 GOSUB 320
140 IF BR THEN PRINT N;:C=C+1
150 N=N+2
160 GOTO 120
170 PRINT:PRINT
180 PRINT "First 12 prime Brazilian numbers:"
190 C=0:N=7
200 IF C>=12 THEN 270
210 GOSUB 320
220 IF BR THEN PRINT N;:C=C+1
230 N=N+2
240 GOSUB 530
250 IF NOT PRM THEN 230
260 GOTO 200
270 PRINT
280 END
290 REM ** Is Brazilian?
300 REM Result: BR=-1 if N is Brazilian
310 REM 0 otherwise
320 IF N<7 THEN BR=0:RETURN
330 IF INT(N/2)*2=N AND N>=8 THEN BR=-1:RETURN
340 FOR B=2 TO N-2
350 GOSUB 430
360 IF SMD THEN BR=-1:RETURN
370 NEXT B
380 BR=0
390 RETURN
400 REM ** Same digits?
410 REM Result: SMD=-1 if N has same digits in B,
420 REM 0 otherwise
430 NL=N:REM "Local" N
440 NDB=INT(NL/B)
450 F=NL-NDB*B
460 NL=NDB:NDB=INT(NL/B)
470 IF NL<=0 THEN SMD=-1:RETURN
480 IF NL-NDB*B<>F THEN SMD=0:RETURN
490 NL=INT(NL/B):NDB=INT(NL/B)
500 GOTO 470
510 REM ** Is prime?
520 REM Result: PRM=-1 if N prime, 0 otherwise
530 IF N<2 THEN PRM=0:RETURN
540 IF INT(N/2)*2=N THEN PRM=N=2:RETURN
550 IF INT(N/3)*3=N THEN PRM=N=3:RETURN
560 D=5
570 IF D*D>N THEN PRM=-1:RETURN
580 IF INT(N/D)*D=N THEN PRM=0:RETURN
590 D=D+2
600 IF INT(N/D)*D=N THEN PRM=0:RETURN
610 D=D+4
620 GOTO 570
</syntaxhighlight>
{{out}}
<pre>
First 20 Brazilian numbers:
7 8 10 12 13 14 15 16 18 20 21 22 24 26 27 28 30 31 32 33
First 20 odd Brazilian numbers:
7 13 15 21 27 31 33 35 39 43 45 51 55 57 63 65 69 73 75 77
First 12 prime Brazilian numbers:
7 13 31 43 73 127 157 211 241 307 421 463
</pre>
==={{header|Visual Basic .NET}}===
{{trans|C#}}
<syntaxhighlight lang="vbnet">Module Module1
Function sameDigits(ByVal n As Integer, ByVal b As Integer) As Boolean
Dim f As Integer = n Mod b : n \= b : While n > 0
If n Mod b <> f Then Return False Else n \= b
End While : Return True
End Function
Function isBrazilian(ByVal n As Integer) As Boolean
If n < 7 Then Return False
If n Mod 2 = 0 Then Return True
For b As Integer = 2 To n - 2
If sameDigits(n, b) Then Return True
Next : Return False
End Function
Function isPrime(ByVal n As Integer) As Boolean
If n < 2 Then Return False
If n Mod 2 = 0 Then Return n = 2
If n Mod 3 = 0 Then Return n = 3
Dim d As Integer = 5
While d * d <= n
If n Mod d = 0 Then Return False Else d += 2
If n Mod d = 0 Then Return False Else d += 4
End While : Return True
End Function
Sub Main(args As String())
For Each kind As String In {" ", " odd ", " prime "}
Console.WriteLine("First 20{0}Brazilian numbers:", kind)
Dim Limit As Integer = 20, n As Integer = 7
Do
If isBrazilian(n) Then Console.Write("{0} ", n) : Limit -= 1
Select Case kind
Case " " : n += 1
Case " odd " : n += 2
Case " prime " : Do : n += 2 : Loop Until isPrime(n)
End Select
Loop While Limit > 0
Console.Write(vbLf & vbLf)
Next
End Sub
End Module</syntaxhighlight>
{{out}}
<pre>First 20 Brazilian numbers:
7 8 10 12 13 14 15 16 18 20 21 22 24 26 27 28 30 31 32 33
First 20 odd Brazilian numbers:
7 13 15 21 27 31 33 35 39 43 45 51 55 57 63 65 69 73 75 77
First 20 prime Brazilian numbers:
7 13 31 43 73 127 157 211 241 307 421 463 601 757 1093 1123 1483 1723 2551 2801
</pre>
====Speedier Version====
Based on the C# speedier version, performance is just as good, one billion Brazilian numbers counted in 4 1/2 seconds (on a core i7).
<syntaxhighlight lang="vbnet">Imports System
Module Module1
' flags:
Const _
PrMk As Integer = 0, ' a number that is prime
SqMk As Integer = 1, ' a number that is the square of a prime number
UpMk As Integer = 2, ' a number that can be factored (aka un-prime)
BrMk As Integer = -2, ' a prime number that is also a Brazilian number
Excp As Integer = 121 ' exception square - the only square prime that is a Brazilian
Dim pow As Integer = 9,
max As Integer ' maximum sieve array length
' An upper limit of the required array length can be calculated Like this:
' power of 10 fraction limit actual result
' 1 2 / 1 * 10 = 20 20
' 2 4 / 3 * 100 = 133 132
' 3 6 / 5 * 1000 = 1200 1191
' 4 8 / 7 * 10000 = 11428 11364
' 5 10/ 9 * 100000 = 111111 110468
' 6 12/11 * 1000000 = 1090909 1084566
' 7 14/13 * 10000000 = 10769230 10708453
' 8 16/15 * 100000000 = 106666666 106091516
' 9 18/17 * 1000000000 = 1058823529 1053421821
' powers above 9 are impractical because of the maximum array length in VB.NET,
' which is around the UInt32.MaxValue, Or 4294967295
Dim PS As SByte() ' the prime/Brazilian number sieve
' once the sieve is populated, primes are <= 0, non-primes are > 0,
' Brazilian numbers are (< 0) or (> 1)
' 121 is a special case, in the sieve it is marked with the BrMk (-2)
' typical sieve of Eratosthenes algorithm
Sub PrimeSieve(ByVal top As Integer)
PS = New SByte(top) {} : Dim i, ii, j As Integer
i = 2 : j = 4 : PS(j) = SqMk : While j < top - 2 : j += 2 : PS(j) = UpMk : End While
i = 3 : j = 9 : PS(j) = SqMk : While j < top - 6 : j += 6 : PS(j) = UpMk : End While
i = 5 : ii = 25 : While ii < top
If PS(i) = PrMk Then
j = (top - i) / i : If (j And 1) = 0 Then j -= 1
Do : If PS(j) = PrMk Then PS(i * j) = UpMk
j -= 2 : Loop While j > i : PS(ii) = SqMk
End If
Do : i += 2 : Loop While PS(i) <> PrMk : ii = i * i
End While
End Sub
' consults the sieve and returns whether a number is Brazilian
Function IsBr(ByVal number As Integer) As Boolean
Return Math.Abs(PS(number)) > SqMk
End Function
' shows the first few Brazilian numbers of several kinds
Sub FirstFew(ByVal kind As String, ByVal amt As Integer)
Console.WriteLine(vbLf & "The first {0} {1}Brazilian Numbers are:", amt, kind)
Dim i As Integer = 7 : While amt > 0
If IsBr(i) Then amt -= 1 : Console.Write("{0} ", i)
Select Case kind : Case "odd " : i += 2
Case "prime " : Do : i += 2 : Loop While PS(i) <> BrMk OrElse i = Excp
Case Else : i += 1 : End Select : End While : Console.WriteLine()
End Sub
' expands a 111_X number into an integer
Function Expand(ByVal NumberOfOnes As Integer, ByVal Base As Integer) As Integer
Dim res As Integer = 1
While NumberOfOnes > 1 AndAlso res < Integer.MaxValue \ Base
res = res * Base + 1 : NumberOfOnes -= 1 : End While
If res > max OrElse res < 0 Then res = 0
Return res
End Function
' returns an elapsed time string
Function TS(ByVal fmt As String, ByRef st As DateTime, ByVal Optional reset As Boolean = False) As String
Dim n As DateTime = DateTime.Now,
res As String = String.Format(fmt, (n - st).TotalMilliseconds)
If reset Then st = n
Return res
End Function
Sub Main(args As String())
Dim p2 As Integer = pow << 1, primes(6) As Integer, n As Integer,
st As DateTime = DateTime.Now, st0 As DateTime = st,
p10 As Integer = CInt(Math.Pow(10, pow)), p As Integer = 10, cnt As Integer = 0
max = CInt(((CLng((p10)) * p2) / (p2 - 1))) : PrimeSieve(max)
Console.WriteLine(TS("Sieving took {0} ms", st, True))
' make short list of primes before Brazilians are added
n = 3 : For i As Integer = 0 To primes.Length - 1
primes(i) = n : Do : n += 2 : Loop While PS(n) <> 0 : Next
Console.WriteLine(vbLf & "Checking first few prime numbers of sequential ones:" &
vbLf & "ones checked found")
' now check the '111_X' style numbers. many are factorable, but some are prime,
' then re-mark the primes found in the sieve as Brazilian.
' curiously, only the numbers with a prime number of ones will turn out, so
' restricting the search to those saves time. no need to wast time on even numbers of ones,
' or 9 ones, 15 ones, etc...
For Each i As Integer In primes
Console.Write("{0,4}", i) : cnt = 0 : n = 2 : Do
If (n - 1) Mod i <> 0 Then
Dim br As Long = Expand(i, n)
If br > 0 Then
If PS(br) < UpMk Then PS(br) = BrMk : cnt += 1
Else
Console.WriteLine("{0,8}{1,6}", n, cnt) : Exit Do
End If
End If : n += 1 : Loop While True
Next
Console.WriteLine(TS("Adding Brazilian primes to the sieve took {0} ms", st, True))
For Each s As String In ",odd ,prime ".Split(",") : FirstFew(s, 20) : Next
Console.WriteLine(TS(vbLf & "Required output took {0} ms", st, True))
Console.WriteLine(vbLf & "Decade count of Brazilian numbers:")
n = 6 : cnt = 0 : Do : While cnt < p : n += 1 : If IsBr(n) Then cnt += 1
End While
Console.WriteLine("{0,15:n0}th is {1,-15:n0} {2}", cnt, n, TS("time: {0} ms", st))
If p < p10 Then p *= 10 Else Exit Do
Loop While (True) : PS = New SByte(-1) {}
Console.WriteLine(vbLf & "Total elapsed was {0} ms", (DateTime.Now - st0).TotalMilliseconds)
If System.Diagnostics.Debugger.IsAttached Then Console.ReadKey()
End Sub
End Module
</syntaxhighlight>
{{out}}
<pre>Sieving took 2967.834 ms
Checking first few prime numbers of sequential ones:
ones checked found
3 32540 3923
5 182 44
7 32 9
11 8 1
13 8 3
17 4 1
19 4 1
Adding Brazilian primes to the sieve took 8.6242 ms
The first 20 Brazilian Numbers are:
7 8 10 12 13 14 15 16 18 20 21 22 24 26 27 28 30 31 32 33
The first 20 odd Brazilian Numbers are:
7 13 15 21 27 31 33 35 39 43 45 51 55 57 63 65 69 73 75 77
The first 20 prime Brazilian Numbers are:
7 13 31 43 73 127 157 211 241 307 421 463 601 757 1093 1123 1483 1723 2551 2801
Required output took 2.8256 ms
Decade count of Brazilian numbers:
10th is 20 time: 0.0625 ms
100th is 132 time: 0.1156 ms
1,000th is 1,191 time: 0.1499 ms
10,000th is 11,364 time: 0.1986 ms
100,000th is 110,468 time: 0.4081 ms
1,000,000th is 1,084,566 time: 1.9035 ms
10,000,000th is 10,708,453 time: 15.9129 ms
100,000,000th is 106,091,516 time: 149.8814 ms
1,000,000,000th is 1,053,421,821 time: 1412.3526 ms
Total elapsed was 4391.7287 ms
</pre>
The point of utilizing a sieve is that it caches or memoizes the results. Since we are going through a long sequence of possible Brazilian numbers, it pays off to check the prime factoring in an efficient way, rather than one at a time.
=={{header|C}}==
{{trans|Go}}
Line 1,173 ⟶ 1,651:
The 100,000th Brazilian number: 110468
</pre>
=={{header|EasyLang}}==
{{trans|C}}
<syntaxhighlight lang="easylang">
func sameDigits n b .
f = n mod b
repeat
n = n div b
until n = 0
if n mod b <> f
return 0
.
.
return 1
.
func isBrazilian7 n .
# n >= 7
if n mod 2 = 0
return 1
.
for b = 2 to n - 2
if sameDigits n b = 1
return 1
.
.
return 0
.
func prime n .
if n mod 2 = 0 and n > 2
return 0
.
i = 3
sq = sqrt n
while i <= sq
if n mod i = 0
return 0
.
i += 2
.
return 1
.
for kind$ in [ "" "odd" "prime" ]
print "First 20 " & kind$ & " Brazilian numbers:"
n = 7
cnt = 1
while cnt <= 20
if isBrazilian7 n = 1
write n & " "
cnt += 1
.
if kind$ = ""
n += 1
elif kind$ = "odd"
n += 2
else
repeat
n += 2
until prime n = 1
.
.
.
print ""
.
</syntaxhighlight>
=={{header|F_Sharp|F#}}==
===The functions===
Line 1,218 ⟶ 1,760:
</pre>
So up to 100,000 ~10% of numbers are non-Brazilian. The millionth Brazilian is 1084566 so less than 10% are non-Brazilian. Large non-Brazilians seem to be rare.
=={{header|Factor}}==
{{works with|Factor|0.99 development release 2019-07-10}}
Line 1,531 ⟶ 2,074:
</pre>
=={{header|Fōrmulæ}}==
{{FormulaeEntry|page=https://formulae.org/?script=examples/Brazilian_numbers}}
'''Solution'''
Function to determine if
[[File:Fōrmulæ - Brazilian numbers 01.png]]
The next function calculates the first Brazilian numbers that agree the given condition. Notice that the condition is provided as a lambda expression:
[[File:Fōrmulæ - Brazilian numbers 02.png]]
'''Test case 1.''' First 20 Brazilian numbers:
[[File:Fōrmulæ - Brazilian numbers 03.png]]
[[File:Fōrmulæ - Brazilian numbers 04.png]]
'''Test case 2.''' First 20 odd Brazilian numbers:
[[File:Fōrmulæ - Brazilian numbers 05.png]]
[[File:Fōrmulæ - Brazilian numbers 06.png]]
'''Test case 3.''' First 20 prime Brazilian numbers:
[[File:Fōrmulæ - Brazilian numbers 07.png]]
[[File:Fōrmulæ - Brazilian numbers 08.png]]
=={{header|Go}}==
===Version 1===
Line 2,567 ⟶ 3,091:
</pre>
[[File:Brazilian densities.png|thumb|center]]
=={{header|Kotlin}}==
{{trans|C#}}
Line 2,761 ⟶ 3,286:
{7, 13, 15, 21, 27, 31, 33, 35, 39, 43, 45, 51, 55, 57, 63, 65, 69, 73, 75, 77}
{7, 13, 31, 43, 73, 127, 157, 211, 241, 307, 421, 463, 601, 757, 1093, 1123, 1483, 1723, 2551, 2801}</pre>
=={{header|MATLAB}}==
{{trans|Mathematica_/_Wolfram_Language}}
<syntaxhighlight lang="MATLAB">
clear all;close all;clc;
% Find the first 20 Brazilian numbers in the range 7 to 100.
brazilian_numbers = [];
for num = 7:100
if brazilianQ(num)
brazilian_numbers = [brazilian_numbers, num];
if length(brazilian_numbers) == 20
break;
end
end
end
% For Brazilian numbers
fprintf('% 8d', brazilian_numbers);
fprintf("\n");
% Find the first 20 odd Brazilian numbers in the range 7 to 100.
odd_brazilian_numbers = [];
for num = 7:100
if brazilianQ(num) && mod(num, 2) ~= 0
odd_brazilian_numbers = [odd_brazilian_numbers, num];
if length(odd_brazilian_numbers) == 20
break;
end
end
end
% For odd Brazilian numbers
fprintf('% 8d', odd_brazilian_numbers);
fprintf("\n");
% Find the first 20 Brazilian prime numbers in the range 7 to 10000.
brazilian_prime_numbers = [];
for num = 7:10000
if brazilianQ(num) && isprime(num)
brazilian_prime_numbers = [brazilian_prime_numbers, num];
if length(brazilian_prime_numbers) == 20
break;
end
end
end
% For Brazilian prime numbers
fprintf('% 8d', brazilian_prime_numbers);
fprintf("\n");
function isBrazilian = brazilianQ(n)
% Function to check if a number is a Brazilian number.
if n <= 6
error('Input must be greater than 6.');
end
isBrazilian = false;
for b = 2:(n-2)
base_b_digits = custom_dec2base(n, b) - '0'; % Convert number to base b and then to digits
if all(base_b_digits == base_b_digits(1))
isBrazilian = true;
break;
end
end
end
function digits = custom_dec2base(num, base)
% Custom function to convert number to any base representation
if base < 2 || base > num
error('Base must be at least 2 and less than the number itself.');
end
digits = [];
while num > 0
remainder = mod(num, base);
digits = [remainder, digits];
num = floor(num / base);
end
end
</syntaxhighlight>
{{out}}
<pre>
7 8 10 12 13 14 15 16 18 20 21 22 24 26 27 28 30 31 32 33
7 13 15 21 27 31 33 35 39 43 45 51 55 57 63 65 69 73 75 77
7 13 31 43 73 127 157 211 241 307 421 463 601 757 1093 1123 1483 1723 2551 2801
</pre>
=={{header|Modula-2}}==
{{trans|C|<code>CARDINAL</code> (unsigned integer) used instead of signed integer.<code>ELSIF</code> used instead of sequential <code>IF</code>s with <code>RETURN</code> s. In the main program, the loop <code>for (i = 0; i < 3; ++i) </code> is replaced by subsequent actions, because the actions vary depending on <code>i</code>.}}
{{works with|ADW Modula-2|any (Compile with the linker option ''Console Application'').}}
<syntaxhighlight lang="modula2">
MODULE BrazilianNumbers;
FROM STextIO IMPORT
WriteLn, WriteString;
FROM SWholeIO IMPORT
WriteInt;
VAR
C, N: CARDINAL;
PROCEDURE SameDigits(N, B: CARDINAL): BOOLEAN;
VAR
F: CARDINAL;
BEGIN
F := N MOD B;
N := N / B;
WHILE N > 0 DO
IF N MOD B <> F THEN
RETURN FALSE;
END;
N := N / B;
END;
RETURN TRUE;
END SameDigits;
PROCEDURE IsBrazilian(N: CARDINAL): BOOLEAN;
VAR
B: CARDINAL;
BEGIN
IF N < 7 THEN
RETURN FALSE
ELSIF (N MOD 2 = 0) AND (N >= 8) THEN
RETURN TRUE
ELSE
FOR B := 2 TO N - 2 DO
IF SameDigits(N, B) THEN
RETURN TRUE
END
END;
RETURN FALSE;
END
END IsBrazilian;
PROCEDURE IsPrime(N: CARDINAL): BOOLEAN;
VAR
D: CARDINAL;
BEGIN
IF N < 2 THEN
RETURN FALSE;
ELSIF N MOD 2 = 0 THEN
RETURN N = 2;
ELSIF N MOD 3 = 0 THEN
RETURN N = 3;
ELSE
D := 5;
WHILE D * D <= N DO
IF N MOD D = 0 THEN
RETURN FALSE
ELSE
D := D + 2;
IF N MOD D = 0 THEN
RETURN FALSE
ELSE
D := D + 4
END
END
END;
RETURN TRUE;
END
END IsPrime;
BEGIN
WriteString("First 20 Brazilian numbers:");
WriteLn;
C := 0; N := 7;
WHILE C < 20 DO
IF IsBrazilian(N) THEN
WriteInt(N, 1);
WriteString(" ");
C := C + 1;
END;
N := N + 1;
END;
WriteLn; WriteLn;
WriteString("First 20 odd Brazilian numbers:");
WriteLn;
C := 0; N := 7;
WHILE C < 20 DO
IF IsBrazilian(N) THEN
WriteInt(N, 1);
WriteString(" ");
C := C + 1;
END;
N := N + 2;
END;
WriteLn; WriteLn;
WriteString("First 20 prime Brazilian numbers:");
WriteLn;
C := 0; N := 7;
WHILE C < 20 DO
IF IsBrazilian(N) THEN
WriteInt(N, 1);
WriteString(" ");
C := C + 1;
END;
REPEAT
N := N + 2
UNTIL IsPrime(N);
END;
WriteLn;
END BrazilianNumbers.
</syntaxhighlight>
{{out}}
<pre>
First 20 Brazilian numbers:
7 8 10 12 13 14 15 16 18 20 21 22 24 26 27 28 30 31 32 33
First 20 odd Brazilian numbers:
7 13 15 21 27 31 33 35 39 43 45 51 55 57 63 65 69 73 75 77
First 20 prime Brazilian numbers:
7 13 31 43 73 127 157 211 241 307 421 463 601 757 1093 1123 1483 1723 2551 2801
</pre>
=={{header|Nim}}==
<syntaxhighlight lang="nim">proc isPrime(n: Positive): bool =
Line 2,842 ⟶ 3,584:
First 20 prime Brazilian numbers:
7, 13, 31, 43, 73, 127, 157, 211, 241, 307, 421, 463, 601, 757, 1093, 1123, 1483, 1723, 2551, 2801</pre>
=={{header|Pascal}}==
{{works with|Free Pascal}}
Line 3,475 ⟶ 4,218:
First 20 prime Brazilians:
[7,13,31,43,73,127,157,211,241,307,421,463,601,757,1093,1123,1483,1723,2551,2801]</pre>
=={{header|Quackery}}==
<code>isprime</code> is defined at [[Primality by trial division#Quackery]].
<syntaxhighlight lang="Quackery"> [ dup base put
/mod temp put
true swap
[ dup 0 > while
base share /mod
temp share != iff
[ dip not ]
done
again ]
drop
temp release
base release ] is allsame ( n n --> b )
[ false swap
dup 3 - times
[ dup i 2 +
allsame iff
[ dip not
conclude ]
done ]
drop ] is brazilian ( n --> b )
say "First 20 Brazilian numbers:" cr
[] 0
[ dup brazilian if
[ dup dip join ]
1+
over size 20 = until ]
drop echo
cr
cr
say "First 20 odd Brazilian numbers:" cr
[] 1
[ dup brazilian if
[ dup dip join ]
2 +
over size 20 = until ]
drop echo
cr
cr
say "First 20 prime Brazilian numbers:" cr
[] 1
[ dup isprime not iff
[ 2 + ] again
dup brazilian if
[ dup dip join ]
2 +
over size 20 = until ]
drop echo</syntaxhighlight>
{{out}}
<pre>First 20 Brazilian numbers:
[ 7 8 10 12 13 14 15 16 18 20 21 22 24 26 27 28 30 31 32 33 ]
First 20 odd Brazilian numbers:
[ 7 13 15 21 27 31 33 35 39 43 45 51 55 57 63 65 69 73 75 77 ]
First 20 prime Brazilian numbers:
[ 7 13 31 43 73 127 157 211 241 307 421 463 601 757 1093 1123 1483 1723 2551 2801 ]
</pre>
=={{header|Racket}}==
Line 3,714 ⟶ 4,524:
done...
</pre>
=={{header|RPL}}==
{{works with|HP|49}}
≪ SWAP OVER IDIV2 ROT → digit base
≪ 1 SF
'''WHILE''' DUP 1 FS? AND '''REPEAT'''
'''IF''' base IDIV2 digit ≠ '''THEN''' 1 CF '''END'''
'''END'''
DROP 1 FS?
≫ ≫ '<span style="color:blue">SAMEDIGITS?</span>' STO
≪ → n
≪ 0
2 n 2 - '''FOR''' b
n b <span style="color:blue">SAMEDIGITS?</span> OR
'''IF''' DUP '''THEN''' n 'b' STO '''END'''
'''NEXT'''
≫ '<span style="color:blue">BRAZILIAN?</span>' STO
≪ → max inc
≪ { } 5
'''DO'''
'''IF''' DUP <span style="color:blue">BRAZILIAN?</span>' '''THEN''' SWAP OVER + SWAP '''END'''
inc EVAL
'''UNTIL''' OVER SIZE max ≥ '''END'''
DROP
≫ '<span style="color:blue">TASK</span>' STO
20 ≪ 1 + ≫ <span style="color:blue">TASK</span>
20 ≪ 2 + ≫ <span style="color:blue">TASK</span>
20 ≪ NEXTPRIME ≫ <span style="color:blue">TASK</span>
{{out}}
<pre>
3: {7 8 10 12 13 14 15 16 18 20 21 22 24 26 27 28 30 31 32 33}
2: {7 13 15 21 27 31 33 35 39 43 45 51 55 57 63 65 69 73 75 77}
1: {7 13 31 43 73 127 157 211 241 307 421 463 601 757 1093 1123 1483 1723 2551 2801}
</pre>
=={{header|Ruby}}==
{{trans|C++}}
Line 3,823 ⟶ 4,670:
First 20 prime Brazilian numbers:
7 13 31 43 73 127 157 211 241 307 421 463 601 757 1093 1123 1483 1723 2551 2801</pre>
=={{header|Rust}}==
<syntaxhighlight lang="rust">
Line 4,059 ⟶ 4,907:
println("be a little patient, it will take some time")
val bigElement = LazyList.from(7).filter(isBrazilian(_)).drop(bigLimit -
println(s"brazilian($bigLimit): $bigElement")
}</syntaxhighlight>
Line 4,069 ⟶ 4,917:
brazilian(100000): 110468
</pre>
=={{header|Sidef}}==
<syntaxhighlight lang="ruby">func is_Brazilian_prime(q) {
Line 4,138 ⟶ 4,987:
1,000,000th Brazilian number = 1084566
</pre>
=={{header|V (Vlang)}}==
{{trans|Go}}
Line 4,474 ⟶ 5,106:
{{trans|Go}}
{{libheader|Wren-math}}
<syntaxhighlight lang="
var sameDigits = Fn.new { |n, b|
Line 4,542 ⟶ 5,174:
The 100,000th Brazilian number: 110468
</pre>
=={{header|XPL0}}==
{{trans|C}}
<syntaxhighlight lang "XPL0">func SameDigits(N, B);
int N, B, F;
[F:= rem(N/B);
N:= N/B;
while N > 0 do
[if rem(N/B) # F then return false;
N:= N/B;
];
return true;
];
func IsBrazilian(N);
int N, B;
[if N < 7 then return false;
if rem(N/2) = 0 and N >= 8 then return true;
for B:= 2 to N-2 do
if SameDigits(N, B) then return true;
return false;
];
func IsPrime(N); \Return 'true' if N is prime
int N, D;
[if N < 2 then return false;
if (N&1) = 0 then return N = 2;
if rem(N/3) = 0 then return N = 3;
D:= 5;
while D*D <= N do
[if rem(N/D) = 0 then return false;
D:= D+2;
if rem(N/D) = 0 then return false;
D:= D+4;
];
return true;
];
int I, C, N, Kinds;
[Kinds:= [" ", " odd ", " prime "];
for I:= 0 to 3-1 do
[Text(0, "First 20"); Text(0, Kinds(I));
Text(0, "Brazilian numbers:^m^j");
C:= 0; N:= 7;
loop [if IsBrazilian(N) then
[IntOut(0, N); ChOut(0, ^ );
C:= C+1;
if C = 20 then
[CrLf(0); CrLf(0); quit];
];
case I of
0: N:= N+1;
1: N:= N+2;
2: repeat N:= N+2 until IsPrime(N)
other [];
];
];
N:= 7; C:= 0;
while C < 100_000 do
[if IsBrazilian(N) then C:= C+1;
N:= N+1;
];
Text(0, "The 100,000th Brazilian number: "); IntOut(0, N-1); CrLf(0);
]</syntaxhighlight>
{{out}}
<pre>
First 20 Brazilian numbers:
7 8 10 12 13 14 15 16 18 20 21 22 24 26 27 28 30 31 32 33
First 20 odd Brazilian numbers:
7 13 15 21 27 31 33 35 39 43 45 51 55 57 63 65 69 73 75 77
First 20 prime Brazilian numbers:
7 13 31 43 73 127 157 211 241 307 421 463 601 757 1093 1123 1483 1723 2551 2801
The 100,000th Brazilian number: 110468
</pre>
=={{header|zkl}}==
<syntaxhighlight lang="zkl">fcn isBrazilian(n){
| |||