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

1, 2, 3, 4, 5, 6, 8, 9, 10, 15, 16, 21, 22, 23, 30, 32, 33, 36, 45, 46, 64, 128, 255, 256, 413, 498, 512, 513, 514, 553, 554, 580, 612, 744, 765, 766, 1024, 1073, 1125, 1162, 1250, 1540, 1544, 2048, 2241, 2413, 2457, 2458, 2522, 2524, 2596, 2754, 2889, 3348, 3352, 3474, 4096

Offset: 1

Author

Michel Marcus, Jan 05 2017

Keywords

• nonn

Comments

A097029 is the subsequence of integers that are fixed points of one iteration.

Up to 10^9, one can find cycles of length: 1, 2, 3, 4, 5, 6, 8, 10, 12, 20.

Links

• Michel Marcus, Table of n, a(n) for n = 1..178
• Michel Marcus, Cycles up to 10^7

Crossrefs

Cf. A000010, A004526.

Cf. A097026, A097027, A097028, A097029.

Cf. A280577.

Programs

PARI

iscycle(v, nextn) = for (i=1, #v, if (v[i] == nextn, return (1); ); ); return (0);
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 ([]);}
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