A117831 Let S_n be the infinite sequence formed by starting with n and repeatedly reversing the digits and adding 4 to get the next term. Sequence gives number of steps for S_n to reach a cycle, or -1 if no cycle is ever reached.

1, 1, 40, 7, 0, 0, 39, 6, 0, 0, 38, 5, 0, 18, 37, 3, 0, 43, 10, 0, 4, 42, 9, 4, 4, 41, 7, 0, 47, 40, 0, 8, 46, 13, 0, 8, 45, 11, 0, 7, 44, 0, 12, 50, 17, 3, 12, 49, 15, 1, 11, 48, 1, 16, 36, 3, 0, 16, 35, 1, 0, 41, 8, 2, 2, 40, 7, 2, 2, 39, 5, 0, 45, 12, 0, 6, 44, 11, 0, 6, 43, 9, 0, 49, 42, 0, 10

Offset

1,3

Comments

It is conjectured that S_n always reaches a cycle.

There are 22 different cycles of length 90 with 4-digit components. I guess that at most half of the numbers between 1000 and 10000 lead to the cycle of length 54 shown in A117830. - Klaus Brockhaus, May 05 2006

Links

Robert Israel, Table of n, a(n) for n = 1..10000

N. J. A. Sloane and others, Sequences of RADD type, OEIS wiki.

Maple

V:= Vector(10^5, -1):
f:= proc(n)
  local L, H, S, i, j, found, x, y;
  global V;
  S:= {n}: H:= n; x:= n;
  for i from 1 to 10^5 do
    if V[x] > -1 then
       for j from 1 to i-1 do V[H[j]]:= i-j+V[x] od;
       return V[n];
    fi;
    L:= convert(x, base, 10);
    x:= add(L[-j]*10^(j-1), j=1..nops(L)) + 4;
    if member(x, S) then
      found:= false; y:= 0;
      V[x]:= 0;
      for j from i by -1 to 1 do
        if H[j] = x then found:= true
        elif not found then V[H[j]]:= 0
        else y:= y+1; V[H[j]]:= y;
        fi
      od;
      return V[n]
    fi;
    H:= H, x;
    S:= S union {x};
  od;
end proc:
map(f, [$1..200]); # Robert Israel, May 07 2020

Crossrefs

S_1 is given in A117828, S_3 in A117829, S_1015 in A117807.

Records are in A118473, A118474.

Full list of sequences on this topic (1): A117230, A117521, A117800, A117816, A117817, A117827, A117828, A117829, A117830, A117831 (this sequence)

Full list of sequences on this topic (2): A117837, A117841, A118473, A118474, A118510, A118511, A118512, A118513, A118514, A118515, A118516

Full list of sequences on this topic (3): A118517-A118533, A118535

Sequence in context: A037937 A126652 A181643 * A152143 A277874 A365051

Adjacent sequences: A117828 A117829 A117830 * A117832 A117833 A117834

Keyword

nonn,base

Author

N. J. A. Sloane, following discussions with Luc Stevens, May 03 2006

Extensions

Corrected and extended by Klaus Brockhaus, May 05 2006

Confirmed by N. J. A. Sloane, May 05 2006

Status

approved