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 A097029 #33 Jan 25 2024 16:36:36
%S A097029 1,2,3,4,8,15,16,32,64,128,255,256,512,1024,2048,4096,8192,16384,
%T A097029 32768,65535,65536,131072,262144,524288,1048576,2097152,4194304,
%U A097029 8388608,16777216,33554432,67108864,83623935,134217728,268435456,536870912,1073741824,2147483648,4294967295
%N A097029 Fixed points when the function f(x) = phi(x) + floor(x/2) is iterated, i.e., solutions to f(x) = x.
%C A097029 Trivial fixed points are the powers of 2. How many nontrivial cases exist like 3, 15, 255, 65535: the first 5 terms of A051179. More?
%C A097029 83623935 is the next such term (see also A050474 and A203966). - _Michel Marcus_, Nov 13 2015
%H A097029 Max Alekseyev, <a href="/A097029/b097029.txt">Table of n, a(n) for n = 1..91</a>
%e A097029 For fixed points the cycle lengths are A097026(n=fix)=1, but the reverse is not true because long transients may also lead to 1-cycles.
%e A097029 So, e.g., 1910 is not here because its terminal 1-cycle is prefixed by a long transient: {1910, 1715, 2033, 2924, 2806, 2723, 3689, 4724, 4722, 3933, 4342, 4163, 6041, 8192, 8192}.
%o A097029 (PARI) isok(n) = eulerphi(n) + n\2 == n; \\ _Michel Marcus_, Nov 13 2015
%Y A097029 Union of A000079 and A050474.
%Y A097029 Cf. A000010, A051179, A097026, A097027, A097028.
%K A097029 nonn
%O A097029 1,2
%A A097029 _Labos Elemer_, Aug 27 2004
%E A097029 a(30)-a(35) from _Michel Marcus_, Nov 13 2015
%E A097029 a(36)-a(38) from _Jinyuan Wang_, Jul 22 2021