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 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. 3

%I

%S 12,14,12,22,12,14,12,20,12,14,12,22,12,14,12,17,12,14,12,20,12,14,12,

%T 40,12,14,12,58,12,14,12,17,12,14,12,33,12,14,12,33,12,14,12,25,12,14,

%U 12,17,12,14,12,33,12,14,12,27,12,14,12,40,12,14,12,17,12,14,12,69,12

%N 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 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 Antti Karttunen, <a href="/A075477/b075477.txt">Table of n, a(n) for n = 0..16384</a>

%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>

%F a(n) = A074473(64n+15), n=0..256. [corrected by _Antti Karttunen_, Oct 09 2018]

%e 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 (PARI)

%o A006370(n) = if(n%2, 3*n+1, n/2);

%o 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(n) = A074473((64*n)+15); \\ _Antti Karttunen_, Oct 09 2018

%Y Cf. A074473, A074474, A075476-A075482, A006370.

%K nonn

%O 0,1

%A _Labos Elemer_, Sep 23 2002

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Last modified May 12 07:28 EDT 2021. Contains 343821 sequences. (Running on oeis4.)