13的可分性规则 thirt

Author: uuk020

thirt/thirt.php

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+<?php
+/**
+ * 13的可分性规则
+ * When you divide the successive powers of 10 by 13 you get the following remainders of the integer divisions:1, 10, 9, 12, 3, 4.
+ * Then the whole pattern repeats.
+ * Hence the following method: Multiply the right most digit of the number with the left most number in the sequence shown above,
+ * the second right most digit to the second left most digit of the number in the sequence. The cycle goes on and you sum all these products.
+ * Repeat this process until the sequence of sums is stationary.
+ * Example: What is the remainder when 1234567 is divided by 13?
+ * 7×1 + 6×10 + 5×9 + 4×12 + 3×3 + 2×4 + 1×1 = 178
+ * We repeat the process with 178:
+ * 8x1 + 7x10 + 1x9 = 87 and again with 87: 7x1 + 8x10 = 87
+ */
+function thirt($n) {
+    $sequence = [1,10,9,12,3,4];
+    $sum = 0;
+    // 将字符串转换为数组, 再把数组相反
+    $arr = array_reverse(str_split($n));
+    // 循环数组
+    for ($i = 0; $i < count($arr); $i++) {
+      // 通过余数来循环出$sequence数组的值 因为$sequence有6个所以除于6求余数.
+      $sum += $arr[$i] * $sequence[$i % 6];
+    }
+    // 判断$n 是否等于$sum, 第一次是不想等, 递归调用 thirt函数, 此时形参$n等于$sum.
+    return ($n === $sum) ? $n : thirt($sum);
+}