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.

%I A117831 #12 May 07 2020 15:35:38
%S A117831 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 A117831 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 A117831 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 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.
%C A117831 It is conjectured that S_n always reaches a cycle.
%C A117831 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 A117831 Robert Israel, <a href="/A117831/b117831.txt">Table of n, a(n) for n = 1..10000</a>
%H A117831 N. J. A. Sloane and others, <a href="/wiki/Sequences_of_RADD_type">Sequences of RADD type</a>, OEIS wiki.
%p A117831 V:= Vector(10^5,-1):
%p A117831 f:= proc(n)
%p A117831   local L, H, S, i, j,found,x,y;
%p A117831   global V;
%p A117831   S:= {n}: H:= n; x:= n;
%p A117831   for i from 1 to 10^5 do
%p A117831     if V[x] > -1 then
%p A117831        for j from 1 to i-1 do V[H[j]]:= i-j+V[x] od;
%p A117831        return V[n];
%p A117831     fi;
%p A117831     L:= convert(x,base,10);
%p A117831     x:= add(L[-j]*10^(j-1),j=1..nops(L)) + 4;
%p A117831     if member(x, S) then
%p A117831       found:= false; y:= 0;
%p A117831       V[x]:= 0;
%p A117831       for j from i by -1 to 1 do
%p A117831         if H[j] = x then found:= true
%p A117831         elif not found then V[H[j]]:= 0
%p A117831         else y:= y+1; V[H[j]]:= y;
%p A117831         fi
%p A117831       od;
%p A117831       return V[n]
%p A117831     fi;
%p A117831     H:= H, x;
%p A117831     S:= S union {x};
%p A117831   od;
%p A117831 end proc:
%p A117831 map(f, [$1..200]); # _Robert Israel_, May 07 2020
%Y A117831 S_1 is given in A117828, S_3 in A117829, S_1015 in A117807.
%Y A117831 Records are in A118473, A118474.
%Y A117831 Full list of sequences on this topic (1): A117230, A117521, A117800, A117816, A117817, A117827, A117828, A117829, A117830, A117831 (this sequence)
%Y A117831 Full list of sequences on this topic (2): A117837, A117841, A118473, A118474, A118510, A118511, A118512, A118513, A118514, A118515, A118516
%Y A117831 Full list of sequences on this topic (3): A118517-A118533, A118535
%K A117831 nonn,base
%O A117831 1,3
%A A117831 _N. J. A. Sloane_, following discussions with Luc Stevens, May 03 2006
%E A117831 Corrected and extended by _Klaus Brockhaus_, May 05 2006
%E A117831 Confirmed by _N. J. A. Sloane_, May 05 2006