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 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. 17

%I

%S 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,

%T 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,

%U 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

%N 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.

%C It is conjectured that S_n always reaches a cycle.

%C 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

%H Robert Israel, <a href="/A117831/b117831.txt">Table of n, a(n) for n = 1..10000</a>

%H N. J. A. Sloane and others, <a href="/wiki/Sequences_of_RADD_type">Sequences of RADD type</a>, OEIS wiki.

%p V:= Vector(10^5,-1):

%p f:= proc(n)

%p local L, H, S, i, j,found,x,y;

%p global V;

%p S:= {n}: H:= n; x:= n;

%p for i from 1 to 10^5 do

%p if V[x] > -1 then

%p for j from 1 to i-1 do V[H[j]]:= i-j+V[x] od;

%p return V[n];

%p fi;

%p L:= convert(x,base,10);

%p if member(x, S) then

%p found:= false; y:= 0;

%p V[x]:= 0;

%p for j from i by -1 to 1 do

%p if H[j] = x then found:= true

%p else y:= y+1; V[H[j]]:= y;

%p fi

%p od;

%p return V[n]

%p fi;

%p H:= H, x;

%p S:= S union {x};

%p od;

%p end proc:

%p map(f, [\$1..200]); # _Robert Israel_, May 07 2020

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

%Y Records are in A118473, A118474.

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

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

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

%K nonn,base

%O 1,3

%A _N. J. A. Sloane_, following discussions with Luc Stevens, May 03 2006

%E Corrected and extended by _Klaus Brockhaus_, May 05 2006

%E Confirmed by _N. J. A. Sloane_, May 05 2006

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Last modified July 14 03:42 EDT 2020. Contains 335716 sequences. (Running on oeis4.)