This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A337673 #20 Jul 19 2023 19:47:36
%S A337673 0,1,2,4,8,16,37,74,172,344,786,1572,3538,7206,16252,33112,73762,
%T A337673 149967,330107,678610,1498356,3082302,6742487,13855154,30122440,
%U A337673 62388962,135783788,281177482,608402189,1259151448,2711432766,5646008216,12172417990,25339969480,54409676729,113159496364
%N A337673 a(n) is the sum of all positive integers whose Collatz orbit has length n.
%C A337673 a(n) >= 2^(n-1) as 2^(n-1) has orbit length n.
%H A337673 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%e A337673 a(6) = 5+32 = 37 as the positive integers whose Collatz orbit has length 6 are {5,32} - the orbit of 5 is 5,16,8,4,2,1, and the orbit of 32 is 32,16,8,4,2,1.
%o A337673 (PARI) nextSet(s) = { my(s1 = Set([])); for(i = 1, #s, s1 = setunion(s1, Set([2*s[i]])); if (s[i] > 4 && (s[i]-1) % 3 == 0 && (s[i]-1)/3 % 2 == 1, s1 = setunion(s1, Set([(s[i]-1)/3]))); ); return(s1); }
%o A337673 a(n) = { my(s = Set([1])); for(k = 1, n, s = nextSet(s); ); return(sum(i=1,#s,s[i])); }
%Y A337673 Cf. A000975, A005186, A153772.
%Y A337673 Equals row sums of triangles A088975 and A127824.
%K A337673 nonn
%O A337673 0,3
%A A337673 _Markus Sigg_, Sep 15 2020
%E A337673 More terms from _David A. Corneth_, Sep 15 2020