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 A306978 Numbers with record number of iterations of x -> A306938(x) required to reach 1 (A306944). 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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 LINKS Table of n, a(n) for n=1..32. H. J. J. te Riele, Iteration of number-theoretic functions, Nieuw Archief v. Wiskunde, (4) 1 (1983), 345-360. See Example III.3. EXAMPLE 2 reaches 1 after 2 iterations: 2 -> 3 -> 1; 4 reaches 1 after a record number of 4 iterations: 4 -> 6 -> 2 -> 3 -> 1. MATHEMATICA 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 CROSSREFS Cf. A306938, A306943, A306944. Sequence in context: A145777 A188497 A237759 * A337062 A153550 A102984 Adjacent sequences: A306975 A306976 A306977 * A306979 A306980 A306981 KEYWORD nonn,more AUTHOR Amiram Eldar, Mar 18 2019 STATUS approved

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Last modified December 4 15:16 EST 2023. Contains 367563 sequences. (Running on oeis4.)