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A306978
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Numbers with record number of iterations of x -> A306938(x) required to reach 1 (A306944).
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0
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1, 2, 4, 7, 21, 49, 85, 253, 442, 766, 1327, 2299, 3982, 11839, 20506, 35518, 61519, 184557, 553645, 966928, 1674769, 2900785, 8701141, 25877593, 44821306, 77676682, 134539960, 402368674, 696922987, 1207106023, 2090768962, 3632578906
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OFFSET
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1,2
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COMMENTS
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The record numbers of iterations are 0, 2, 4, 6, 7, 8, 10, 11, 13, 15, 17, 19, 21, 22, 24, 26, 28, 29, 30, 32, 34, 36, 37, 38, 40, 42, 44, 45, 47, 49, 51, 53.
Conjecture: sqrt(3) < a(n)/a(n-1) <= 3. - Daniel Suteu, Mar 20 2019
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LINKS
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EXAMPLE
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2 reaches 1 after 2 iterations: 2 -> 3 -> 1;
4 reaches 1 after a record number of 4 iterations: 4 -> 6 -> 2 -> 3 -> 1.
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MATHEMATICA
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f[n_] := If[Divisible[n, 3], n/3, Floor[n*Sqrt[3]]]; itnum[n_] := Module[{k = n, inc = False, c = 0}, While[k > 1, kk = f[k]; If[inc && kk > k, c = -1; Break[]]; inc = kk > k; k = kk; c++]; c]; s={}; im=-1; Do[i=itnum[n]; If[i>im, im=i; AppendTo[s, n]], {n, 1, 10000}]; s
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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