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Task/Sisyphus-sequence/00-TASK.txt

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+The '''Sisyphus sequence''' is an infinite sequence of positive integers that was devised in 2022 by Eric Angelini and Carole Dubois.
+
+The first term is 1. Subsequent terms are found by applying the following rule:
+
+* If the previous term was even, then halve it.
+
+* If the previous term was odd, then add the smallest prime number that has not yet been added.
+
+1 is odd and so the second term is: 1 + 2 = 3, because 2 is the smallest prime not yet added.
+
+3 is odd and so the third term is: 3 + 3 = 6, because 3 is the smallest prime not yet added.
+
+6 is even and so the fourth term is : 6 ÷ 2 = 3, and so on.
+
+;Task
+Find and show on this page (in 10 lines of 10 terms), the first 100 terms of the sequence.
+
+What are the '''1,000'''th, '''10,000'''th, '''100,000'''th  and '''1,000,000'''th terms of the sequence and, in each case, what is the highest prime needed to reach them?
+
+If it is difficult or impossible for your language or output device to meet all of these requirements, then just do what you reasonably can. 
+
+;Stretch
+What are the '''10 millionth''' and '''100 millionth''' terms and the highest prime needed to reach each one?
+
+By the time the '''100 millionth''' term is reached, which number(s) '''under 250''':
+
+* Have not yet occurred in the sequence.
+
+* Have occurred the most times and their number of occurrences.
+
+
+;Extreme stretch
+What is the number of the first term to equal 36?
+
+This was originally set as a challenge by Neil Sloane who was worried by its non-appearance and found by Russ Cox. 
+
+;References
+* OEIS sequence [[oeis:A350877|A350877: The Sisyphus sequence]] 
+<br>
+