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A343156
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Starting at n, a(n) = number of iterations of the map x -> A084317(x) (concatenate distinct prime factors of x) required to reach a prime, or -1 if no prime is ever reached.
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4
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0, 0, 1, 0, 1, 0, 1, 1, 2, 0, 1, 0, 2, 4, 1, 0, 1, 0, 2, 1, 1, 0, 1, 1, 4, 1, 2, 0, 2, 0, 1, 1, 5, 3, 1, 0, 2, 1, 2, 0, 2, 0, 1, 4, 1, 0, 1, 1, 2, 1, 4, 0, 1, 2, 2, 2, 1, 0, 2, 0, 3, 1, 1, 3, 1, 0, 5, 3, 1, 0, 1, 0, 2, 4, 2, 2, 2, 0, 2, 1, 1, 0, 2, 3, 2, 3, 1, 0, 2, 64, 1, 1, 2, 4, 1, 0, 2, 1, 2
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OFFSET
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2,9
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COMMENTS
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Judging by the behavior of similar sequences, it is likely that almost all values of a(n) are -1. n = 407 (see A343157) seems to be the first open case.
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REFERENCES
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Eric Angelini, W. Edwin Clark, Hans Havermann, Frank Stevenson, Allan C. Wechsler, and others, Postings to Math Fun mailing list, April 2021.
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LINKS
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EXAMPLE
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10 = 2*5 -> 25 = 5^2 -> 5, prime, taking two steps, so a(10)=2.
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CROSSREFS
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See A343158 for when k first appears.
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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