

A280578


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


1



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
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OFFSET

1,2


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


PROG

(PARI) 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, print1(#v, ", "); known = vecsort(concat(known, v))); ); print(known); }


CROSSREFS

Cf. A000010, A004526.
Cf. A097026, A097027, A097028, A097029.
Cf. A280577.
Sequence in context: A226857 A256007 A324689 * A303878 A039170 A097624
Adjacent sequences: A280575 A280576 A280577 * A280579 A280580 A280581


KEYWORD

nonn


AUTHOR

Michel Marcus, Jan 05 2017


STATUS

approved



