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A280578 Integers that are fixed points of some iteration of f(x) = phi(x) + floor(x/2), see A280577.

%I A280578 #30 Mar 15 2022 08:20:24
%S A280578 1,2,3,4,5,6,8,9,10,15,16,21,22,23,30,32,33,36,45,46,64,128,255,256,
%T A280578 413,498,512,513,514,553,554,580,612,744,765,766,1024,1073,1125,1162,
%U A280578 1250,1540,1544,2048,2241,2413,2457,2458,2522,2524,2596,2754,2889,3348,3352,3474,4096
%N A280578 Integers that are fixed points of some iteration of f(x) = phi(x) + floor(x/2), see A280577.
%C A280578 A097029 is the subsequence of integers that are fixed points of one iteration.
%C A280578 Up to 10^9, one can find cycles of length: 1, 2, 3, 4, 5, 6, 8, 10, 12, 20.
%H A280578 Michel Marcus, <a href="/A280578/b280578.txt">Table of n, a(n) for n = 1..178</a>
%H A280578 Michel Marcus, <a href="/A280578/a280578.txt">Cycles up to 10^7</a>
%o A280578 (PARI) iscycle(v, nextn) = for (i=1, #v, if (v[i] == nextn, return (1); ); ); return (0);
%o A280578 fcycle(n, known) = {v = vector(1); v[1] = n; first = n; while ((nextn = eulerphi(n) + n\2) <= first, if (vecsearch(known, nextn), return([])); if (iscycle(v, nextn), return (v)); v = concat(v, nextn); n = nextn; ); return ([]);}
%o A280578 lista(nn) = {known = []; for (n = 1, nn, v = fcycle(n, known); if (#v, known = vecsort(concat(known, v)));); print(known);} \\ corrected by _Michel Marcus_, Mar 15 2022
%Y A280578 Cf. A000010, A004526.
%Y A280578 Cf. A097026, A097027, A097028, A097029.
%Y A280578 Cf. A280577.
%K A280578 nonn
%O A280578 1,2
%A A280578 _Michel Marcus_, Jan 05 2017