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A097027 Function f(x) = phi(x) + floor(x/2) is iterated; a(n) is the length of transient if the iteration was initiated at n. 5
0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 2, 3, 0, 0, 4, 1, 3, 2, 0, 0, 0, 3, 1, 2, 2, 3, 2, 0, 1, 0, 0, 1, 3, 0, 2, 3, 17, 1, 2, 1, 16, 2, 0, 0, 18, 2, 19, 1, 2, 2, 17, 1, 15, 3, 1, 2, 15, 1, 19, 20, 15, 0, 4, 18, 14, 19, 17, 16, 21, 2, 20, 21, 30, 22, 29, 16, 27, 3, 24, 25, 14, 19, 22, 23, 14, 20, 23 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,13

COMMENTS

Infinite iterations cannot be excluded, when a(n) is infinite. First at n=163?

For 1 <= n <= 1000, potentially infinite iterations at {163, 182, 196, 243, 283, 331, 423, 487, 495, 503, 511, 523, 533, 551, 559, 571, 583, 591, 593, 606, 611, 623, 642, 646, 651, 679, 685, 687, 725, 726, 729, 731, 732, 745, 746, 753, 755, 757, 758, 767, 779, 781, 783, 791, 799, 809, 811, 814, 839, 850, 855, 857, 859, 867, 869, 871, 875, 876, 885, 886, 888, 891, 895, 906, 908, 911, 913, 914, 915, 916, 921, 922, 923, 931, 937, 942, 959, 962, 964, 970, 971, 977, 985, 991} (tested to 1000 iterations). The maximum number of finite iterations in this range appears to be 96. - Michael De Vlieger, Mar 26 2017

LINKS

Table of n, a(n) for n=1..89.

EXAMPLE

n=70: iteration list = [70, 59, 87, 99, 109, 162, 135, 139, 207, 235, 301, 402, 333, 382, 381, 442, [413, 554, 553, 744, 612, 498], 413], so a(70)=16.

n=2^j: a(2^j)=0, powers of 2 are fixed points of f, free of transients.

MAPLE

a:= proc(n) local i, m, p;

      p:= proc() -1 end; forget(p);

      p(n):= 0; m:= n;

      for i do m:= numtheory[phi](m)+iquo(m, 2);

               if p(m)>-1 then return p(m) fi;

               p(m):= i

      od

    end:

seq(a(n), n=1..162);  # Alois P. Heinz, Nov 13 2015

MATHEMATICA

Table[Count[Values@ PositionIndex@ NestList[EulerPhi@ # + Floor[#/2] &, n, 10^3], k_ /; Length@ k == 1], {n, 89}] (* Michael De Vlieger, Mar 26 2017, Version 10 *)

CROSSREFS

Cf. A000010, A097026, A097028, A097029.

Sequence in context: A234017 A182057 A260928 * A072741 A131360 A338780

Adjacent sequences:  A097024 A097025 A097026 * A097028 A097029 A097030

KEYWORD

nonn

AUTHOR

Labos Elemer, Aug 27 2004

STATUS

approved

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Last modified June 16 21:55 EDT 2021. Contains 345080 sequences. (Running on oeis4.)