Data update

Task/Magic-constant/C++/magic-constant.cpp

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+#include <cmath>
+#include <cstdint>
+#include <iomanip>
+#include <iostream>
+#include <string>
+
+constexpr int32_t ORDER_FIRST_MAGIC_SQUARE = 3;
+constexpr double LN2 = log(2.0);
+constexpr double LN10 = log(10.0);
+
+// Return the magic constant for a magic square of the given order
+int32_t magicConstant(int32_t n) {
+	return n * ( n * n + 1 ) / 2;
+}
+
+// Return the smallest order of a magic square such that its magic constant is greater than 10 to the given power
+int32_t minimumOrder(int32_t n) {
+	return (int) exp( ( LN2 + n * LN10 ) / 3 ) + 1;
+}
+
+// Return the order of the magic square at the given index
+int32_t order(int32_t index) {
+	return ORDER_FIRST_MAGIC_SQUARE + index - 1;
+}
+
+int main() {
+	std::cout << "The first 20 magic constants:" << std::endl;
+	for ( int32_t i = 1; i <= 20; ++i ) {
+		std::cout << " " << magicConstant(order(i));
+	}
+	std::cout << std::endl << std::endl;
+
+	std::cout << "The 1,000th magic constant: " << magicConstant(order(1'000)) << std::endl << std::endl;
+
+	std::cout << "Order of the smallest magic square whose constant is greater than:" << std::endl;
+	for ( int32_t i = 1; i <= 20; ++i ) {
+		std::string power_of_10 = "10^" + std::to_string(i) + ":";
+		std::cout << std::setw(6) << power_of_10 << std::setw(8) << minimumOrder(i) << std::endl;
+	}
+}

Task/Magic-constant/Java/magic-constant.java

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+public final class MagicConstant {
+
+	public static void main(String[] aArgs) {
+		System.out.println("The first 20 magic constants:");
+		for ( int i = 1; i <= 20; i++ ) {
+			System.out.print(" " + magicConstant(order(i)));
+		}
+		System.out.println(System.lineSeparator());
+		
+		System.out.println("The 1,000th magic constant: " + magicConstant(order(1_000)) + System.lineSeparator());
+		
+		System.out.println("Order of the smallest magic square whose constant is greater than:");
+		for ( int i = 1; i <= 20; i++ ) {
+			String powerOf10 = "10^" + i + ":";
+			System.out.println(String.format("%6s%8s", powerOf10, minimumOrder(i)));
+		}
+	}
+	
+	// Return the magic constant for a magic square of the given order
+	private static int magicConstant(int aN) {	
+		return aN * ( aN * aN + 1 ) / 2;
+	}
+
+	// Return the smallest order of a magic square such that its magic constant is greater than 10 to the given power
+	private static int minimumOrder(int aN) {		
+		return (int) Math.exp( ( LN2 + aN * LN10 ) / 3 ) + 1;
+	}
+	
+	// Return the order of the magic square at the given index
+	private static int order(int aIndex) {
+		return ORDER_FIRST_MAGIC_SQUARE + aIndex - 1;
+	}
+	
+    private static final int ORDER_FIRST_MAGIC_SQUARE = 3;
+	private static final double LN2 = Math.log(2.0);
+	private static final double LN10 = Math.log(10.0);
+
+}

Task/Magic-constant/Lua/magic-constant.lua

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+function magic (x)
+    return x * (1 + x^2) / 2
+end
+
+print("Magic constants of orders 3 to 22:")
+for i = 3, 22 do
+    io.write(magic(i) .. " ")
+end
+
+print("\n\nMagic constant 1003: " .. magic(1003) .. "\n")
+
+print("Orders of smallest magic constant greater than...")
+print("-----\t-----\nValue\tOrder\n-----\t-----")
+local order = 1
+for i = 1, 20 do
+    repeat
+        order = order + 1
+    until magic(order) > 10 ^ i
+    print("10^" .. i, order)
+end