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 A304123 #15 May 08 2018 02:42:07
%S A304123 1,32,2048,8192,2199023255552,144115188075855872,576460752303423488,
%T A304123 2305843009213693952
%N A304123 Denominators of records low values of the ratio n*3^A006667(n)/2^A006666(n).
%e A304123 For n=1 to 10 the ratios are 1, 1, 27/32, 1, 15/16, 27/32, 1701/2048, 1, 6561/8192, 15/16, so the low records are 1, 27/32, 1701/2048, 6561/8192, ...
%t A304123 q=1;Collatz[n_]:=NestWhileList[If[EvenQ[#],#/2,3 #+1]&,n,#>1&];nn=5000;t={};n=0;While[Length[t]<nn,n++;c=Collatz[n];ev=Length[Select[c,EvenQ]];od=Length[c]-ev-1;If[n*3^od/2^ev<q,Print[n," ",od," ",ev," ",n*3^od/2^ev];q=n*3^od/2^ev]]
%o A304123 (PARI) ht(n) = my(h, t); while(n>1, if(n%2, n=3*n+1; t++, n>>=1; h++)); return([h, t]);
%o A304123 lista(nn) = {m = 2; for (n=1, nn, v = ht(n); newm = n*3^v[2]/2^v[1]; if (newm < m, print1(denominator(newm), ", "); m = newm)); } \\ _Michel Marcus_, May 06 2018
%Y A304123 Cf. A127789 (for the indices where these records occur).
%Y A304123 Cf. A304119 (for the corresponding numerators).
%Y A304123 Cf. A006666, A006667.
%K A304123 nonn,frac,more
%O A304123 1,2
%A A304123 _Michel Lagneau_, May 06 2018