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%I #22 Jan 16 2022 11:08:41
%S 1,3,4,8,6,6,14,14,15,9,12,20,21,21,22,30,28,33,22,11,16,34,31,23,32,
%T 30,25,43,32,29,35,40,31,58,49,47,39,43,45,46,39,44,32,44,22,56,51,61,
%U 48,46,55,68,69,60,69,70,78,89,72,93,61,64,80,71,60,58,71
%N Number of steps to reach an integer starting with (2^n + 1)/2^n and iterating the map x->x*ceiling(x).
%C Is a(n) > n for n > 10? Does lim_{n->infinity} a(n)/n exist?
%C a(n) <= n for n = 1, 6, 10, 20, 21, 24, 27, ... - _Amiram Eldar_, Nov 28 2020
%t a[n_] := Module[{x = (2^n + 1)/2^n, nstep = 0}, While[!IntegerQ[x], nstep++; x *= Ceiling[x]]; nstep]; Array[a, 15] (* _Amiram Eldar_, Nov 28 2020 *)
%Y Cf. A073524.
%K nonn
%O 1,2
%A _Benoit Cloitre_, Sep 17 2002
%E a(16)-a(17) from _Ryan Propper_, Mar 18 2008
%E a(18)-a(21) from _Lars Blomberg_, Jan 17 2013
%E a(22)-a(27) from _Amiram Eldar_, Nov 28 2020
%E More terms from _Jinyuan Wang_, Jan 15 2022