For any natural number n, when n is odd, add 121, and when n is even, divide by 2, which counts as one operation. Now, if the three-digit number 241 is operated continuously, will 100 appear during the operation, why?
对于任意一个自然数n，当n为奇数时，加上121，当n为偶数时，除以2，这算一次操作．现在对三位数241连续进行操作，在操作过程中是否会出现100，为什么？
<gadget id="calculator">241 + 121</gadget>
<output>362</output>

<gadget id="calculator">362 / 2</gadget>
<output>181</output>

<gadget id="calculator">181 + 121</gadget>
<output>302</output>

<gadget id="calculator">302 / 2</gadget>
<output>151</output>

<gadget id="calculator">151 + 121</gadget>
<output>272</output>

<gadget id="calculator">272 / 2</gadget>
<output>136</output>

<gadget id="calculator">136 / 2</gadget>
<output>68</output>

<gadget id="calculator">68 / 2</gadget>
<output>34</output>

<gadget id="calculator">34 / 2</gadget>
<output>17</output>

<gadget id="calculator">17 + 121</gadget>
<output>138</output>

<gadget id="calculator">138 / 2</gadget>
<output>69</output>

<gadget id="calculator">69 + 121</gadget>
<output>190</output>

<gadget id="calculator">190 / 2</gadget>
<output>95</output>

<gadget id="calculator">95 + 121</gadget>
<output>216</output>

<gadget id="calculator">216 / 2</gadget>
<output>108</output>

<gadget id="calculator">108 / 2</gadget>
<output>54</output>

<gadget id="calculator">54 / 2</gadget>
<output>27</output>

<gadget id="calculator">27 + 121</gadget>
<output>148</output>

<gadget id="calculator">148 / 2</gadget>
<output>74</output>

<gadget id="calculator">74 / 2</gadget>
<output>37</output>

<gadget id="calculator">37 + 121</gadget>
<output>158</output>

<gadget id="calculator">158 / 2</gadget>
<output>79</output>

<gadget id="calculator">79 + 121</gadget>
<output>200</output>

<gadget id="calculator">200 / 2</gadget>
<output>100</output>

<result>100</result>