A118512 -id:A118512 - cp's OEIS frontend

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

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

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

Robert Israel, Table of n, a(n) for n = 1..10000
N. J. A. Sloane and others, Sequences of RADD type, OEIS wiki.

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

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

Corrected and extended by Klaus Brockhaus, May 05 2006

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

A118513 Define sequence S_m by: initial term = m, reverse digits and add 1 to get next term. Entry shows S_13. This reaches a cycle of length 9 in 15 steps.

Original entry on oeis.org

13, 32, 24, 43, 35, 54, 46, 65, 57, 76, 68, 87, 79, 98, 90, 10, 2, 3, 4, 5, 6, 7, 8, 9, 10, 2, 3, 4, 5, 6, 7, 8, 9, 10, 2, 3, 4, 5, 6, 7, 8, 9, 10, 2, 3, 4, 5, 6, 7, 8, 9, 10, 2, 3, 4, 5, 6, 7, 8, 9, 10, 2, 3, 4, 5, 6, 7, 8, 9, 10, 2, 3, 4, 5, 6, 7, 8, 9, 10, 2, 3, 4, 5, 6, 7, 8, 9, 10

Offset: 1

N. J. A. Sloane, May 06 2006

N. J. A. Sloane and others, Sequences of RADD type, OEIS wiki.
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 1).

Cf. A118510, A117831, A117230, A118512.

Join[{13,32,24,43,35,54,46,65,57,76,68,87,79,98,90},LinearRecurrence[{0,0,0,0,0,0,0,0,1},{10,2,3,4,5,6,7,8,9},73]] (* Ray Chandler, Jul 18 2015 *)
NestList[IntegerReverse[#]+1&,13,90] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 06 2019 *)

A118511 Define sequence S_n by: initial term = n, reverse digits and add 1 to get next term. It is conjectured that S_n always reaches a cycle of length 9, as in A117230. Sequence gives number of steps for S_n to reach the cycle.

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18, 17, 15, 13, 11, 9, 7, 5, 3, 1, 16, 16, 15, 13, 11, 9, 7, 5, 3, 1, 14, 14, 14, 13, 11, 9, 7, 5, 3, 1, 12, 12, 12, 12, 11, 9, 7, 5, 3, 1, 10, 10, 10, 10, 10, 9, 7, 5, 3, 1, 8, 8, 8, 8, 8, 8, 7, 5, 3, 1, 6, 6, 6, 6, 6, 6, 6, 5, 3, 1, 4, 4, 4, 4, 4, 4, 4

Offset: 1

N. J. A. Sloane, May 06 2006

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

For records see A118510. Cf. A117831. S_1 is A117230, S_11 is A118512, S_13 is A118513.

cp's OEIS Frontend

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.

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A118513 Define sequence S_m by: initial term = m, reverse digits and add 1 to get next term. Entry shows S_13. This reaches a cycle of length 9 in 15 steps.

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A118511 Define sequence S_n by: initial term = n, reverse digits and add 1 to get next term. It is conjectured that S_n always reaches a cycle of length 9, as in A117230. Sequence gives number of steps for S_n to reach the cycle.

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