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 A260593 #12 Oct 24 2015 12:06:23
%S A260593 4,2,7,5,59,56,8,54,51,45,42,31,15,40,21,29,13,12,20,27,24,10,16,18,
%T A260593 23,39,81,35,37,26,80,34,78,43,32,61,58,50,48,46,70,65,69,53,64,77,73,
%U A260593 72,105,75,67,83,62,92,135,126,86,111,129,124,123,127,88,119,108,100
%N A260593 The values of the modified Syracuse algorithm, msa, in the order in which they appear in A260590.
%C A260593 See A260590 for the definition of the msa.
%C A260593 Sorted: 2, 4, 5, 7, 8, 10, 12, 13, 15, 16, 18, 20, 21, 23, 24, 26, 27, 29, 31, 32, 34, 35, 37, 39, 40, 42, 43, 45, 46, 48, 50, 51, 53, 54, 56, 58, 59, 61, 62, 64, 65, 67, 69, 70, 72, 73, 75, 77, 78, 80, 81, 83, 85, 86, 88, 89, 91, 92, 94, 96, 97, 99, 100, ... (A020914(n) for n>0).
%C A260593 Record values: 4, 7, 59, 81, 105, 135, 164, 165, 173, 176, 183, 224, 246, 287, 292, 298, 308, 376, 395, 398, 433, 447, ... .
%C A260593 Record last values to appear: 2, 5, 8, 10, 16, 18, 23, 26, 32, 46, 53, 62, 85, 94, 99, 102, 107, 115, 118, 130, 132, 134, 148, ... .
%e A260593 Every odd number greater than 1 yields a msa value. a(1) is 4 and it corresponds to A260590(1).
%e A260593 a(2) is 2 since A260590(2) is 2.
%e A260593 a(3) is 7 since A260590(3) is 7.
%e A260593 a(4) is 5 since A260590(5) is 5, A260590(4) is 2 but it already appears as a(2).
%t A260593 msa[n_] := If[ OddQ@ n, (3n + 1)/2, n/2]; f[n_] := Block[{k = 2n + 1}, Length@ NestWhileList[ msa@# &, k, # >= k &] - 1]; k = 1; lst = {}; While[k < 10000001, a = f@ k; If[ !MemberQ[lst, a], AppendTo[lst, a]]; k++]; lst
%Y A260593 Cf. A260590, A260594.
%K A260593 nonn,easy
%O A260593 1,1
%A A260593 Joseph K. Horn and _Robert G. Wilson v_, Aug 30 2015