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A087717
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Start with x=n, then iterate the map x -> A322982(x) with A322982(x)=2*x-1 if x is noncomposite, otherwise A322982(x) = A032742(x), the largest proper divisor of x. If this iteration leads to a fixed point then a(n) is the value of that fixed point. If the iteration leads to a cycle, a(n) is the smallest value in the cycle. If the iteration never becomes periodic then a(n)=0.
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3
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1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 19, 3, 3, 3, 3, 3, 3, 3, 3, 3, 19, 3, 3, 3, 3, 3, 3, 3, 19, 19, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 19, 19, 3, 3, 3, 3, 3, 3, 3, 3, 19, 3, 3, 3, 3, 3, 19, 19, 3, 19, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 19, 3, 3, 3, 3, 3, 3, 3, 19, 3, 3, 3, 3, 3
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OFFSET
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1,2
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COMMENTS
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Conjecture. For n > 1, the iteration given in the definition above always leads to the 3-cycle {3,5,9,3} or the 6-cycle {19,37,73,145,29,57,19}, thus a(n) takes on only the values 3 or 19 for n=2,3,4,.... This has been verified to n=1000000.
In range 2..100000 term 3 occurs 77630 times, while 19 occurs 22369 times. - Antti Karttunen, Jan 03 2019
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LINKS
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MATHEMATICA
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Which[Length@ Union@ #[[-2 ;; -1]] == 1, Last@ #, MemberQ[{3, 5, 9}, Last@ #], 3, MemberQ[{19, 37, 73, 145, 29, 57}, Last@ #], 19, True, 0] & /@ Array[NestWhileList[If[CompositeQ@ #, Divisors[#][[-2]], 2 # - 1] &, #, UnsameQ[##] &, All] &, 106] (* Michael De Vlieger, Jan 03 2019 *)
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PROG
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(PARI)
A322982(n) = if((1==n)||isprime(n), n+n-1, n/vecmin(factor(n)[, 1]));
A087717(n) = { my(visited = Map(), visited_at_step = Map(), j=0, m=0, t); while(!mapisdefined(visited, n), mapput(visited, n, j); mapput(visited_at_step, j, n); j++; n = A322982(n)); for(k=mapget(visited, n), j-1, t = mapget(visited_at_step, k); if(!m || (t<m), m=t)); (m); }; \\ Antti Karttunen, Jan 03 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Name edited and the term a(1) = 1 prepended by Antti Karttunen, Jan 03 2019
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STATUS
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approved
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