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 A076228 #24 Dec 28 2021 09:04:34
%S A076228 0,1,2,2,3,5,4,3,6,5,6,8,6,9,6,4,8,13,10,7,5,11,8,10,13,9,9,15,13,10,
%T A076228 9,5,16,11,8,19,17,16,17,8,12,7,19,15,13,11,12,11,19,20,17,11,9,17,14,
%U A076228 19,23,18,21,15,13,16,14,6,22,24,21,14,12,11,15,22,18,21,7,21,19,25,22,9
%N A076228 Number of terms k in the trajectory of the Collatz function applied to n such that k < n.
%C A076228 It is believed that for each x, a(n) = x occurs a finite number of times and the largest n is 2^x.
%C A076228 Original name: Start iteration of Collatz-function (A006370) with initial value of n. a(n) shows how many times during fixed-point-list, the value sinks below initial one until reaching endpoint = 1. - _Michael De Vlieger_, Dec 13 2018
%H A076228 Michael De Vlieger, <a href="/A076228/b076228.txt">Table of n, a(n) for n = 1..10000</a>
%H A076228 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%e A076228 A070165(18) = {18, 9, 28, 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1}. a(18) = 13 because 13 terms are smaller than n = 18; namely: {9, 14, 7, 11, 17, 13, 10, 5, 16, 8, 4, 2, 1}.
%t A076228 f[x_] := (1-Mod[x, 2])*(x/2)+(Mod[x, 2])*(3*x+1) f[1]=1; f0[x_] := Delete[FixedPointList[f, x], -1] f1[x_] := f0[x]-Part[f0[x], 1] f2[x_] := Count[Sign[f1[x]], -1] Table[f2[w], {w, 1, 256}]
%t A076228 (* Second program: *)
%t A076228 Table[Count[NestWhileList[If[EvenQ@ #, #/2, 3 # + 1] &, n, # > 1 &], _?(# < n &)], {n, 80}] (* _Michael De Vlieger_, Dec 09 2018 *)
%Y A076228 Cf. A006370, A070165, A074473, A159999.
%K A076228 nonn
%O A076228 1,3
%A A076228 _Labos Elemer_, Oct 01 2002