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A151963
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(Length of preperiodic part) + (length of cycle) of trajectory of n under iteration of the Kaprekar map in A151949.
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10
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1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 3, 7, 5, 6, 4, 4, 6, 5, 7, 3, 2, 3, 7, 5, 6, 4, 4, 6, 5, 7, 3, 2, 3, 7, 5, 6, 4, 4, 6, 5, 7, 3, 2, 3, 7, 5, 6, 4, 4, 6, 5, 7, 3, 2, 3, 7, 5, 6, 4, 4, 6, 5, 7, 3, 2, 3, 7, 5, 6, 4, 4, 6, 5, 7, 3, 2, 3, 7, 5, 6, 4, 4, 6, 5, 7, 3, 2, 3, 7, 5, 6, 4, 4, 6, 5, 7, 3
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OFFSET
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0,2
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COMMENTS
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Equals A151962(n) + 1 iff n < 10001 (when a cycle of length greater than 1 occurs for the first time).
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LINKS
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Joseph Myers and Robert G. Wilson v, Table of n, a(n) for n = 0..1000 .
Index entries for the Kaprekar map
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EXAMPLE
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13->18->63->27->45->9->0->0, so a(13)=6+1 = 7.
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MAPLE
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# Maple program from R. J. Mathar:
A151949 := proc(n)
local tup;
tup := sort(convert(n, base, 10)) ;
add( (op(i, tup)-op(-i, tup)) *10^(i-1), i=1..nops(tup)) :
end:
A151963 := proc(n)
local tra, x ;
tra := [n] ;
x := n ;
while true do
x := A151949(x) ;
if x in tra then
RETURN(nops(tra)) ;
fi;
tra := [op(tra), x] :
od:
end:
seq(A151963(n), n=0..120) ;
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MATHEMATICA
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f[n_] := Module[{idn = IntegerDigits@n, idns}, idns = Sort@ idn; FromDigits@ Reverse@ idns - FromDigits@ idns]; g[n_] := Length[ NestWhileList[ f, n, UnsameQ, All]] - 1; Table[g@n, {n, 0, 104}] (* Robert G. Wilson v, Aug 20 2009 *)
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CROSSREFS
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In other bases: A164886 (base 2), A164996 (base 3), A165015 (base 4), A165035 (base 5), A165054 (base 6), A165074 (base 7), A165093 (base 8), A165113 (base 9). - Joseph Myers, Sep 05 2009
Sequence in context: A307713 A328680 A256707 * A191291 A131841 A309432
Adjacent sequences: A151960 A151961 A151962 * A151964 A151965 A151966
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KEYWORD
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nonn,base
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AUTHOR
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N. J. A. Sloane, Aug 19 2009
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EXTENSIONS
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Typos corrected by Joseph Myers, Aug 20 2009
More terms from R. J. Mathar and Robert G. Wilson v, Aug 20 2009
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STATUS
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approved
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