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Look at these two sequences.
The rules of these two sequences are the same.

0 32 15 3 9 5 4 2 6 7 13 110 174 155 314 2120 5360 24671 119546 193002 240820 274454 153700 1397287 17916598 26245242 8880928 7320921 14726415 42969065 35308126 14978764 68756682 ...

8 11 94 58 10 49 57 ___ 1272 8699 3292 3332 48033 90311 112817 1149731 24909936 1838500 5264650 29232231 76236585 64535680 49758988 191873638 ...

Question 1: What is the missing number?

Find it.

Question 2: What will happen if you start up a sequence with the number $12$ and
continue the sequence using the same rule?

Write down the sequence.

Question 3: Is there a number greater than $2$ that can cause an infinite loop
in the sequence if you start the sequence with the number and continue with the rule?

If yes, write the number down.

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  • $\begingroup$ When l cIicked the "Post your question" button, it kept me waiting for a long time, posted the question and then said that an error occurred. $\endgroup$
    – Scratch---Cat
    Mar 14, 2020 at 12:32
  • $\begingroup$ AIso, l wonder if the "seasonal" tag is suitable here. This is my first "number-sequence" question and I wonder if I'm aIIowed to post number sequences. $\endgroup$
    – Scratch---Cat
    Mar 14, 2020 at 12:35
  • $\begingroup$ Please read question 2 & 3 before you want to close this question. $\endgroup$
    – Scratch---Cat
    Mar 14, 2020 at 12:41

1 Answer 1

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The rule is:

$a_{n+1}$ is the position of first occurrence of $a_{n}$ in Pi. You can check it at here.

Question 1:

404 - also an HTTP status code of Not Found :)

Question 2:

12, 148, 103, 3486, 265, 6, 7, ... (same as the first sequence)

Question 3:

The number 1 definitely cause an infinite loop. Therefore the numbers 14, 141, 1415, ... also cause an infinite loop from the second term(1).

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