cp's OEIS Frontend

A075476 Number of iteration that first becomes smaller than the initial value if Collatz-function (A006370) is iterated, starting with numbers of form 64n+7. Corresponds to selection of every 16th term from A074474.

%I A075476 #14 Oct 09 2018 15:11:12
%S A075476 12,84,12,14,12,35,12,14,12,17,12,14,12,25,12,14,12,25,12,14,12,27,12,
%T A075476 14,12,17,12,14,12,38,12,14,12,25,12,14,12,45,12,14,12,17,12,14,12,27,
%U A075476 12,14,12,20,12,14,12,79,12,14,12,17,12,14,12,20,12,14,12,33,12,14,12
%N A075476 Number of iteration that first becomes smaller than the initial value if Collatz-function (A006370) is iterated, starting with numbers of form 64n+7. Corresponds to selection of every 16th term from A074474.
%C A075476 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 A075476 Antti Karttunen, <a href="/A075476/b075476.txt">Table of n, a(n) for n = 0..16384</a>
%H A075476 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%F A075476 a(n) = A074473(64n+7), n=0, ..., 256
%e A075476 n=0: 64n+7=7, list={7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5..}, i.e. the 12th term is the first that <12, the initial value.
%t A075476 lcoll[n_] := Length[NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # >= n &]]; Table[lcoll[64*i + 7], {i, 0, 68}] (* _Jayanta Basu_, Jun 15 2013 *)
%o A075476 (PARI)
%o A075476 A006370(n) = if(n%2, 3*n+1, n/2);
%o A075476 A074473(n) = if(1==n,n,my(org_n=n); for(i=1,oo,if(n<org_n, return(i)); n = A006370(n)));
%o A075476 A075476(n) = A074473((64*n)+7); \\ _Antti Karttunen_, Oct 09 2018
%Y A075476 Cf. A074473, A074474, A006370.
%K A075476 nonn
%O A075476 0,1
%A A075476 _Labos Elemer_, Sep 23 2002
%E A075476 Typo in formula corrected by _Antti Karttunen_, Oct 09 2018