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A075480 Number of iteration that first becomes smaller than the initial value if Collatz function (A006370) is iterated, starting with numbers of the form 64n + 39.

%I A075480 #14 Feb 23 2019 19:37:12
%S A075480 14,69,48,20,14,27,17,33,14,20,22,40,14,58,20,17,14,33,22,33,14,64,17,
%T A075480 33,14,71,20,35,14,40,43,17,14,71,71,25,14,27,17,40,14,22,25,27,14,43,
%U A075480 25,17,14,66,27,25,14,76,17,20,14,22,43,27,14,66,25,17,14,22
%N A075480 Number of iteration that first becomes smaller than the initial value if Collatz function (A006370) is iterated, starting with numbers of the form 64n + 39.
%C A075480 Initial values of the form 64m + r, if r = {3,11,19,27,35,43,51,55}, provide first-sink-lengths {7,9,7,9,7,9,7,9} respectively; e.g., {64k + 19, 192k + 58, 96k + 29, 288k + 88, 144k + 44, 72k + 22, 36k + 11} submerge first below initial value at the 7th term, 36k + 11 < 64k + 19.
%H A075480 Nathaniel Johnston, <a href="/A075480/b075480.txt">Table of n, a(n) for n = 0..10000</a>
%F A075480 a(n) = A074473(64n+39).
%e A075480 n=0: 64n + 39 = 39, Collatz trajectory = {39, 118, 59, 178, 89, 268, 134, 67, 202, 101, 304, 152, 76, 38, 19, 58, ....}, i.e., the 14th term = 38 is the first that is less than 39, the initial value, so a(0)=14.
%p A075480 col := proc(n) if(n mod 2 = 0)then return n/2: fi: return 3*n+1: end: A075480 := proc(n) local s,v: s:=1: v:=64*n+39: while v>=64*n+39 do v:=col(v): s:=s+1: od: return s: end: seq(A075480(n),n=0..65); # _Nathaniel Johnston_, Jun 22 2011
%Y A075480 Cf. A074473, A074474, A075476-A075483, A006370.
%K A075480 easy,nonn
%O A075480 0,1
%A A075480 _Labos Elemer_, Sep 23 2002
%E A075480 Keyword:fini removed by _Nathaniel Johnston_, Jun 23 2011
%E A075480 Edited by _Jon E. Schoenfield_, Feb 23 2019