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%I #6 Feb 20 2017 23:15:41
%S 7,12,9,12,7,9,97,92,7,14,9,89,7,9,12,89,7,84,9,14,7,9,74,14,7,69,9,
%T 51,7,9,14,25,7,12,9,12,7,9,66,35,7,48,9,14,7,9,12,22,7,14,9,22,7,9,
%U 14,51,7,20,9,33,7,9,45,22,7,12,9,12,7,9,40,17,7,14,9,22,7,9,12,35,7,35,9,14
%N Number of iteration that first becomes smaller than the initial value if Collatz-function (A006370) is iterated, starting with numbers of form 4n+3.
%F a(n)=A074473[4n-1]
%e n=6: 4n-1=23, the list={23,70,35,106,53,160,80,40,20, 10,5,16,8,4,2,1} sinks first below iv=23 at 20, the 9th term, so a(6)=9. Observe several (provable) modular rules with respect of initial value: e.g. regular appearance of 9 and 7.
%t Table[Function[k, Length@ NestWhileList[If[EvenQ@ #, #/2, 3 # + 1] &, k, # >= k &]][4 n - 1], {n, 120}] (* _Michael De Vlieger_, Feb 20 2017 *)
%Y Cf. A006370, A074472, A074473.
%K nonn
%O 1,1
%A _Labos Elemer_, Sep 19 2002
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