Data Update

Task/Blum-integer/C++/blum-integer.cpp

@@ -0,0 +1,68 @@
+#include <algorithm>
+#include <cstdint>
+#include <iomanip>
+#include <iostream>
+#include <vector>
+
+bool is_prime_type_3(const int32_t number) {
+	if ( number < 2 ) return false;
+	if ( number % 2 == 0 ) return false;
+	if ( number % 3 == 0 ) return number == 3;
+
+	for ( int divisor = 5; divisor * divisor <= number; divisor += 2 ) {
+		if ( number % divisor == 0 ) { return false; }
+	}
+
+	return number % 4 == 3;
+}
+
+int32_t least_prime_factor(const int32_t number) {
+	if ( number == 1 ) { return 1; }
+    if ( number % 3 == 0 ) { return 3; }
+    if ( number % 5 == 0 ) { return 5; }
+
+    for ( int divisor = 7; divisor * divisor <= number; divisor += 2 ) {
+		if ( number % divisor == 0 ) { return divisor; }
+	}
+
+	return number;
+}
+
+int main() {
+	int32_t blums[50];
+	int32_t blum_count = 0;
+	int32_t last_digit_counts[10] = {};
+	int32_t number = 1;
+
+	while ( blum_count < 400'000 ) {
+		const int32_t prime = least_prime_factor(number);
+		if ( prime % 4 == 3 ) {
+			const int32_t quotient = number / prime;
+			if ( quotient != prime && is_prime_type_3(quotient) ) {
+				if ( blum_count < 50 ) {
+					blums[blum_count] = number;
+				}
+				last_digit_counts[number % 10] += 1;
+				blum_count += 1;
+				if ( blum_count == 50 ) {
+					std::cout << "The first 50 Blum integers:" << std::endl;
+					for ( int32_t i = 0; i < 50; ++i ) {
+						std::cout << std::setw(3) << blums[i] << ( ( i % 10 == 9 ) ? "\n" : " " );
+					}
+					std::cout << std::endl;
+				} else if ( blum_count == 26'828 || blum_count % 100'000 == 0 ) {
+					std::cout << "The " << std::setw(6) << blum_count << "th Blum integer is: "
+						<< std::setw(7) << number << std::endl;
+					if ( blum_count == 400'000 ) {
+						std::cout << "\nPercent distribution of the first 400000 Blum integers:" << std::endl;
+						for ( const int32_t& i : { 1, 3, 7, 9 } ) {
+							std::cout << "    " << std::setw(6) << std::setprecision(5)
+								<< (double) last_digit_counts[i] / 4'000 << "% end in " << i << std::endl;
+						}
+					}
+				}
+			}
+		}
+		number += ( number % 5 == 3 ) ? 4 : 2;
+	}
+}

Task/Blum-integer/Java/blum-integer.java

@@ -0,0 +1,69 @@
+import java.util.HashMap;
+import java.util.Map;
+
+public final class BlumInteger {
+
+	public static void main(String[] aArgs) {
+		int[] blums = new int[50];
+		int blumCount = 0;
+		Map<Integer, Integer> lastDigitCounts = new HashMap<Integer, Integer>();
+		int number = 1;
+		
+		while ( blumCount < 400_000 ) {			
+			final int prime = leastPrimeFactor(number);
+			if ( prime % 4 == 3 ) {
+				final int quotient = number / prime;
+				if ( quotient != prime && isPrimeType3(quotient) ) {
+					if ( blumCount < 50 ) {
+						blums[blumCount] = number;
+					}
+					lastDigitCounts.merge(number % 10, 1, Integer::sum);
+					blumCount += 1;
+					if ( blumCount == 50 ) {
+						System.out.println("The first 50 Blum integers:");
+						for ( int i = 0; i < 50; i++ ) {
+							System.out.print(String.format("%3d", blums[i]));
+							System.out.print(( i % 10 == 9 ) ? System.lineSeparator() : " ");
+						}
+						System.out.println();
+					} else if ( blumCount == 26_828 || blumCount % 100_000 == 0 ) {
+						System.out.println(String.format("%s%6d%s%7d",
+							"The ", blumCount, "th Blum integer is: ", number));
+						if ( blumCount == 400_000 ) {
+							System.out.println();
+							System.out.println("Percent distribution of the first 400000 Blum integers:");
+							for ( int key : lastDigitCounts.keySet() ) {
+		            			System.out.println(String.format("%s%6.3f%s%d",
+		            				"    ", (double) lastDigitCounts.get(key) / 4_000, "% end in ", key));
+							}
+						}
+					}
+				}
+			}
+			number += ( number % 5 == 3 ) ? 4 : 2;
+		}
+	}
+	
+	private static boolean isPrimeType3(int aNumber) {
+		if ( aNumber < 2 ) { return false; }
+		if ( aNumber % 2 == 0 ) { return false; }
+		if ( aNumber % 3 == 0 ) { return aNumber == 3; }
+
+		for ( int divisor = 5; divisor * divisor <= aNumber; divisor += 2 ) {
+			if ( aNumber % divisor == 0 ) { return false; }
+		}		
+		return aNumber % 4 == 3;
+	}
+
+	private static int leastPrimeFactor(int aNumber) {
+		if ( aNumber == 1 ) { return 1; }
+	    if ( aNumber % 3 == 0 ) { return 3; }
+	    if ( aNumber % 5 == 0 ) { return 5; }
+	
+	    for ( int divisor = 7; divisor * divisor <= aNumber; divisor += 2 ) {
+	    	if ( aNumber % divisor == 0 ) { return divisor; }
+	    }	
+		return aNumber;
+	}
+
+}

Task/Blum-integer/Ruby/blum-integer.rb

@@ -0,0 +1,15 @@
+require 'prime'
+
+BLUM_EXP = [1, 1]
+blums = (1..).step(2).lazy.select do |c|
+  next if c % 5 == 0
+  primes, exps = c.prime_division.transpose
+  exps == BLUM_EXP && primes.all?{|pr| (pr-3) % 4 == 0}
+end
+
+n, m = 50, 26828
+res =  blums.first(m)
+puts "First #{n} Blum numbers:"
+res.first(n).each_slice(10){|s| puts "%4d"*s.size % s}
+
+puts "\n#{m}th Blum number: #{res.last}"