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A117831
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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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17
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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
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1,3
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COMMENTS
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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
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LINKS
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MAPLE
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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:
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CROSSREFS
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Full list of sequences on this topic (2): A117837, A117841, A118473, A118474, A118510, A118511, A118512, A118513, A118514, A118515, A118516
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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