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A075483 Number of iteration that first becomes smaller than the initial value if Collatz-function (A006370) is iterated, starting with numbers of form 64n+63.

%I A075483 #10 Feb 20 2017 23:16:08
%S A075483 89,25,22,22,35,20,66,30,17,38,133,27,25,40,35,30,20,25,22,38,38,133,
%T A075483 51,27,17,40,22,30,20,35,22,95,131,33,20,25,27,22,27,66,17,27,71,45,
%U A075483 33,48,35,89,22,33,30,30,48,22,40,30,17,61,30,64,22,22,25,84,22,22,25,33
%N A075483 Number of iteration that first becomes smaller than the initial value if Collatz-function (A006370) is iterated, starting with numbers of form 64n+63.
%C A075483 1stSubmergeLengths[=A074473] with initial values belonging to other residue classes modulo 64 are either listed in A075476-A075483 or can be easily determined. For 64k+2s the first sink below initial value is at 2nd iterate; for 64k+4s+1 the first submerge below initial value comes at 4th term of iteration list; finally if initial value is of 64k+4s+3 form or moreover initial value = 64k+r, r = 3, 11, 19, 23, 35, 43, 51, 55, then for all k first sink emerges at the 7th, 9th, 7th, 9th, 7th, 9th, 7th, 9th iterates, respectively.
%F A075483 a(n) = A074473(64n + 63).
%e A075483 n=8: 64n + 63 = 575, the list = the 17th term 410 < 575 = initial value, so a(8)=17.
%t A075483 Table[Function[k, Length@ NestWhileList[If[EvenQ@ #, #/2, 3 # + 1] &, k, # >= k &]][64 n - 1], {n, 120}] (* _Michael De Vlieger_, Feb 20 2017 *)
%Y A075483 Cf. A006370, A074472, A074473, A075476-A075482.
%K A075483 nonn
%O A075483 0,1
%A A075483 _Labos Elemer_, Sep 24 2002