cp's OEIS Frontend

A075477 Number of iteration that first becomes smaller than the initial value if Collatz-function (A006370) is iterated, starting with numbers of form 64n+15. Corresponds to selection of every 16th term from A074474.

%I A075477 #12 Oct 09 2018 15:14:38
%S A075477 12,14,12,22,12,14,12,20,12,14,12,22,12,14,12,17,12,14,12,20,12,14,12,
%T A075477 40,12,14,12,58,12,14,12,17,12,14,12,33,12,14,12,33,12,14,12,25,12,14,
%U A075477 12,17,12,14,12,33,12,14,12,27,12,14,12,40,12,14,12,17,12,14,12,69,12
%N A075477 Number of iteration that first becomes smaller than the initial value if Collatz-function (A006370) is iterated, starting with numbers of form 64n+15. Corresponds to selection of every 16th term from A074474.
%C A075477 Remark that initial values of 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 A075477 Antti Karttunen, <a href="/A075477/b075477.txt">Table of n, a(n) for n = 0..16384</a>
%H A075477 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%F A075477 a(n) = A074473(64n+15), n=0..256. [corrected by _Antti Karttunen_, Oct 09 2018]
%e A075477 n=0: 64n+15=15,list={15,46,23,70,35,106,53,160,80,40,20,10..}, i.e. the 12th term is the first that <15, the initial value.
%o A075477 (PARI)
%o A075477 A006370(n) = if(n%2, 3*n+1, n/2);
%o A075477 A074473(n) = if(1==n,n,my(org_n=n); for(i=1,oo,if(n<org_n, return(i)); n = A006370(n)));
%o A075477 A075477(n) = A074473((64*n)+15); \\ _Antti Karttunen_, Oct 09 2018
%Y A075477 Cf. A074473, A074474, A075476-A075482, A006370.
%K A075477 nonn
%O A075477 0,1
%A A075477 _Labos Elemer_, Sep 23 2002