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A368690
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Number of terms in the trajectory from n to 2 of the map x -> A368241(x), or -1 if n never reaches 2.
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0
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5, 2, 4, 2, 8, 3, 9, 6, 7, 2, 8, 7, 10, 6, 9, 2, 7, 6, 9, 6, 17, 8, 16, 8, 6, 5, 8, 2, 3, 16, 7, 15, 7, 5, 9, 10, 7, 6, 8, 2, 15, 6, 14, 6, 5, 10, 8, 9, 6, 5, 7, 7, 16, 3, 14, 5, 13, 2, 14, 4, 9, 7, 8, 5, 5, 13, 6, 6, 15, 2, 13, 11, 10, 12, 28, 5, 13, 3, 8, 6, 7, 15, 3, 4, 12, 5
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OFFSET
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4,1
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COMMENTS
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It is conjectured that every starting n reaches 2 eventually.
A368241(x) decreases to the prime gap x-prevprime(x) when x is prime, or increases to x+primepi(x) otherwise, and will reach 2 when x is the greater of a twin prime pair (A006512, preceding prime gap 2).
Prime gaps and x+primepi(x) may become large, but if the twin prime conjecture is true then there would be large twin primes they might reach too.
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LINKS
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EXAMPLE
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For n=4 the trajectory is 4 -> 6 -> 9 -> 13 -> 2 (row 4 of A368196) which has a(4) = 5 terms.
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PROG
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(PARI) f(n) = if (isprime(n), n - precprime(n-1), n + primepi(n)); \\ A368241
a(n) = my(k=1); while ((n = f(n)) != 2, k++); k+1; \\ Michel Marcus, Jan 03 2024
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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