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
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