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A281665 Numbers m such that A006667(m)/A006577(m) = 1/3.

%I A281665 #19 Jan 31 2017 21:19:37
%S A281665 159,283,377,502,503,603,615,668,669,670,799,807,888,890,892,893,1063,
%T A281665 1065,1095,1186,1187,1188,1189,1190,1417,1435,1580,1581,1582,1585,
%U A281665 1586,1587,1889,1913,1947,1959,1963,2104,2106,2108,2109,2113,2114,2115,2119,2518
%N A281665 Numbers m such that A006667(m)/A006577(m) = 1/3.
%C A281665 A006667: number of tripling steps to reach 1 in '3x+1' problem.
%C A281665 A006577: number of halving and tripling steps to reach 1 in '3x+1' problem.
%C A281665 The corresponding number of iterations A006577(a(n)) is given by the sequence 54, 60, 63, 66, 66, 69, 69, 69, 69, 69, 72, 72, 72, 72, 72, 72, 75, 75, ... and the set of the distinct values of this sequence is {b(n)} = {54, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99, 102, 105, 108, 111, 114, 117, 120, ...}. We observe that {b(k)} = {54} union {60 + 3*k} for k = 1, 2, ...
%H A281665 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%e A281665 159 is in the sequence because A006667(159)/A006577(159) = 18/54 = 1/3.
%p A281665 nn:=10000:
%p A281665 for n from 2 to 3000 do:
%p A281665   m:=n:s1:=0:s2:=0:
%p A281665    for i from 1 to nn while(m<>1) do:
%p A281665     if irem(m,2)=0
%p A281665      then
%p A281665      s2:=s2+1:m:=m/2:
%p A281665      else
%p A281665      s1:=s1+1:m:=3*m+1:
%p A281665     fi:
%p A281665    od:
%p A281665    s:=s1/(s1+s2):
%p A281665     if s=1/3
%p A281665      then
%p A281665      printf(`%d, `,n):
%p A281665      else
%p A281665     fi:
%p A281665 od:
%Y A281665 Cf. A006577, A006666, A006667.
%K A281665 nonn
%O A281665 1,1
%A A281665 _Michel Lagneau_, Jan 31 2017