

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



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
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OFFSET

1,3


COMMENTS

It is conjectured that S_n always reaches a cycle.
There are 22 different cycles of length 90 with 4digit 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 i1 do V[H[j]]:= ij+V[x] od;
return V[n];
fi;
L:= convert(x, base, 10);
x:= add(L[j]*10^(j1), 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): A118517A118533, A118535
Sequence in context: A037937 A126652 A181643 * A152143 A277874 A033975
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



