Add example programs (project euler)

examples/euler1.nek

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+// If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. 
+// The sum of these multiples is 23.
+// Find the sum of all the multiples of 3 or 5 below 1000.
+// 
+// Correct Answer: 233168
+
+sum <- 0;
+i <- 0;
+loop i < 1_000; i = i + 1 {
+    if i % 3 == 0 | i % 5 == 0 {
+        sum = sum + i;
+    }
+}
+
+print sum;

examples/euler2.nek

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+// Each new term in the Fibonacci sequence is generated by adding the previous two terms. 
+// By starting with 1 and 2, the first 10 terms will be:
+//   1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...
+// By considering the terms in the Fibonacci sequence whose values do not exceed four million, 
+// find the sum of the even-valued terms.
+// 
+// Correct Answer: 4613732
+
+sum <- 0;
+
+a <- 0;
+b <- 1;
+tmp <- 0;
+
+loop a < 4_000_000 {
+    if a % 2 == 0 {
+        sum = sum + a;
+    }
+
+    tmp = a;
+    a = b;
+    b = b + tmp;
+}
+
+print sum;
+

examples/euler3.nek

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+// The prime factors of 13195 are 5, 7, 13 and 29.
+// What is the largest prime factor of the number 600851475143 ?
+// 
+// Correct Answer: 6857
+
+number <- 600_851_475_143;
+result <- 0;
+
+div <- 2;
+
+loop number > 1 {
+    loop number % div == 0 {
+        if div > result {
+            result = div;
+        }
+        number = number / div;
+    }
+
+    div = div + 1;
+    if div * div > number {
+        if number > 1 & number > result {
+            result = number;
+        }
+        number = 0;
+    }
+
+}
+
+print result;

examples/euler4.nek

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+// A palindromic number reads the same both ways. The largest palindrome made from the product of 
+// two 2-digit numbers is 9009 = 91 × 99.
+// Find the largest palindrome made from the product of two 3-digit numbers.
+// 
+// Correct Answer: 906609
+
+
+res <- 0;
+
+tmp <- 0;
+num <- 0;
+num_rev <- 0;
+
+i <- 100;
+k <- 100;
+loop i < 1_000; i = i + 1 {
+    k = 100;
+    loop k < 1_000; k = k + 1 {
+        num_rev = 0;
+
+        num = i * k;
+
+        tmp = num;
+
+        loop tmp {
+            num_rev = num_rev*10 + tmp % 10;
+            tmp = tmp / 10;
+        }
+
+        if num == num_rev & num > res {
+            res = num;
+        }
+    }
+}
+
+print res;

examples/euler4.py

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+# A palindromic number reads the same both ways. The largest palindrome made from the product of 
+# two 2-digit numbers is 9009 = 91 × 99.
+# Find the largest palindrome made from the product of two 3-digit numbers.
+# 
+# Correct Answer: 906609
+
+
+res = 0
+
+for i in range(100, 999):
+    for k in range(100, 999):
+
+        num = i * k
+        tmp = num
+
+        num_rev = 0
+        while tmp != 0:
+            num_rev = num_rev*10 + tmp % 10
+            tmp = tmp // 10
+        
+        if num == num_rev and num > res:
+            res = num
+
+print(res)