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 A222598 #13 Mar 03 2013 13:56:25
%S A222598 5,3,7,15,159,27,127,255,511,1023,1819,4095,4255,16383,32767,65535,
%T A222598 77671,262143,459759,1048575,2097151,4194303,7456539,16777215,
%U A222598 33554431,67108863,134217727,268435455,125687199,1073741823,2147483647,4294967295,8589934591
%N A222598 Least number k having Collatz (3x+1) sequence with exactly n pairs of odd and even numbers in a row.
%C A222598 This sequence is very similar to A213215. It is somewhat surprising that many of these numbers are of the form 2^k - 1. Note that this is true for n = 2, 3, 4, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 31, 32, and 33; not true for n = 1, 5, 6, 11, 13, 17, 19, 23, and 29.
%e A222598 The Collatz sequence of 15 is 15, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1. It begins with 4 pairs of odd/even numbers.
%t A222598 Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; countOnes[t_] := Module[{mx = 0, cnt = 0, i = 0}, While[i < Length[t], i++; If[t[[i]] == 1, cnt++; i++, If[cnt > mx, mx = cnt]; cnt = 0]]; mx]; nn = 15; t = Table[0, {nn}]; t[[1]] = 1; n = 1; While[Min[t] == 0, n = n + 2; c = countOnes[Mod[Collatz[n], 2]]; If[c <= nn && t[[c]] == 0, t[[c]] = n]]; t
%Y A222598 Cf. A213215.
%K A222598 nonn
%O A222598 1,1
%A A222598 _T. D. Noe_, Mar 02 2013
%E A222598 a(24)-a(33) from _Donovan Johnson_, Mar 03 2013