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A375937 Odd numbers which are the largest odd number in their Collatz trajectory.

%I A375937 #15 Sep 05 2024 14:13:52
%S A375937 1,5,13,17,21,29,33,37,45,49,53,61,65,69,77,81,85,93,101,113,117,133,
%T A375937 141,149,157,173,177,181,197,205,209,213,229,237,241,245,261,269,273,
%U A375937 277,289,301,305,309,317,321,325,341,349,357,369,373,385,397,401,405
%N A375937 Odd numbers which are the largest odd number in their Collatz trajectory.
%C A375937 a(n) == 1 (mod 4) because the trajectory of 4x+3 is (4x+3, 12x+10, 6x+5, ...) and 6x+5 > 4x+3.
%H A375937 Markus Sigg, <a href="/A375937/b375937.txt">Table of n, a(n) for n = 1..10000</a>
%F A375937 a(n) = (A176869(n) - 1) / 3 for n > 1.
%e A375937 The odd elements of the Collatz trajectory (3,10,5,16,8,4,2,1) are {3,5,1} with maximum 5 > 3, so 3 is not a term. The odd elements of the Collatz trajectory (13,40,20,10,5,16,8,4,2,1) are {13,5,1} with maximum 13, so 13 is a term.
%o A375937 (PARI)
%o A375937 makeEntries(count) = {
%o A375937     my(L = List(), k = 1);
%o A375937     while(#L < count,
%o A375937         my(m = k);
%o A375937         while(m > 1 && m <= k,
%o A375937             m = 3*m + 1;
%o A375937             while(m % 2 == 0, m = m / 2);
%o A375937         );
%o A375937         if(m == 1, listput(L, k));
%o A375937         k += 2
%o A375937     );
%o A375937     L
%o A375937 };
%o A375937 print(Vec(makeEntries(56)));
%Y A375937 Cf. A033496, A176869.
%K A375937 nonn
%O A375937 1,2
%A A375937 _Markus Sigg_, Sep 03 2024