A308006 Iterate the map x->A308005(x) starting at x=n; a(n) is the number of steps before the first repeated term is encountered.

3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 0, 2, 1, 2, 1, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 1

Offset

0,1

Links

Robert Israel, Table of n, a(n) for n = 0..10000

Example

0 -> 11 -> 220 -> 33 -> 220 -> ... and a number is repeated at step 4, so a(0)=3.
1 -> 110 -> 231 -> 231 -> 231 -> ..., so a(1) = 2.
22 -> 22 -> 22 -> ... is a fixed point, so a(22) = 0.

Maple

# using Maple procedure A308006 from that sequence
f:= proc(n) local t, S, i;
  S:= {n};
  t:= n;
  do
    t:= A308005(t);
    if member(t, S) then return nops(S)-1 fi;
    S:= S union {t};
  od
end proc:
map(f, [$0..100]); # Robert Israel, May 14 2019

Crossrefs

Cf. A308005.

Sequence in context: A097509 A095206 A344129 * A049071 A168330 A176059

Adjacent sequences: A308003 A308004 A308005 * A308007 A308008 A308009

Keyword

nonn,base

Author

N. J. A. Sloane, May 12 2019

Status

approved