A165093 -id:A165093 - cp's OEIS frontend

A164886 (Length of preperiodic part) + (length of cycle) of trajectory of n under iteration of the base-2 Kaprekar map in A164884.

1, 2, 3, 2, 3, 3, 3, 2, 3, 1, 2, 3, 2, 3, 3, 2, 3, 2, 2, 2, 2, 1, 2, 3, 2, 2, 2, 3, 2, 3, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 3, 2, 1, 2, 2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 3, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2

Offset: 0

Joseph Myers, Aug 29 2009

All base-2 cycles are fixed points, so one more than A164885.

Joseph Myers, Table of n, a(n) for n = 0..1024
Index entries for the Kaprekar map

Cf. A164884, A163205, A164885, A164887.

In other bases: A164996 (base 3), A165015 (base 4), A165035 (base 5), A165054 (base 6), A165074 (base 7), A165093 (base 8), A165113 (base 9), A151963 (base 10).

Cross-references edited by Joseph Myers, Sep 04 2009

A151963 (Length of preperiodic part) + (length of cycle) of trajectory of n under iteration of the Kaprekar map in A151949.

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane, Aug 19 2009

Equals A151962(n) + 1 iff n < 10001 (when a cycle of length greater than 1 occurs for the first time).

			13->18->63->27->45->9->0->0, so a(13)=6+1 = 7.

Joseph Myers and Robert G. Wilson v, Table of n, a(n) for n = 0..1000 .
Index entries for the Kaprekar map

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

# 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) ;

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 *)

Typos corrected by Joseph Myers, Aug 20 2009

More terms from R. J. Mathar and Robert G. Wilson v, Aug 20 2009

A164996 (Length of preperiodic part) + (length of cycle) of trajectory of n under iteration of the base-3 Kaprekar map in A164993.

Original entry on oeis.org

1, 2, 2, 3, 2, 3, 3, 3, 2, 3, 3, 4, 3, 2, 3, 4, 3, 3, 4, 4, 4, 4, 3, 3, 4, 3, 2, 3, 3, 4, 3, 3, 2, 4, 3, 4, 3, 3, 3, 3, 2, 3, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 2, 3, 3, 4, 4, 4, 3, 4, 4, 4, 3, 4, 3, 4, 3, 3, 3, 4, 3, 3, 4, 4, 3, 4, 3, 3, 3, 3, 2, 3, 3, 2, 3, 3, 2, 2, 2, 3, 3, 3, 2, 3, 3, 4, 2, 4, 2, 2, 2, 3, 2, 4, 2

Offset: 0

Joseph Myers, Sep 04 2009

Joseph Myers, Table of n, a(n) for n=0..2187
Index entries for the Kaprekar map

Cf. A164993, A164995.

In other bases: A164886 (base 2), A165015 (base 4), A165035 (base 5), A165054 (base 6), A165074 (base 7), A165093 (base 8), A165113 (base 9), A151963 (base 10).

A165015 (Length of preperiodic part) + (length of cycle) of trajectory of n under iteration of the base-4 Kaprekar map in A165012.

Original entry on oeis.org

1, 2, 2, 2, 3, 2, 3, 4, 4, 3, 2, 3, 4, 4, 3, 2, 3, 3, 2, 3, 3, 2, 3, 2, 2, 3, 3, 2, 3, 2, 1, 2, 2, 2, 2, 3, 2, 3, 3, 2, 2, 3, 2, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 3, 2, 3, 3, 3, 2, 3, 2, 3, 3, 3, 2, 3, 3, 3, 4, 3, 3, 3, 2, 2, 4, 2, 4, 3, 3, 3, 4, 3, 2, 3, 3, 3, 3, 3, 3, 4, 3, 3, 4, 3, 3, 3, 2, 3, 3, 3, 3, 3

Offset: 0

Joseph Myers, Sep 04 2009

Joseph Myers, Table of n, a(n) for n = 0..1024
Index entries for the Kaprekar map

Cf. A165012, A165014.

In other bases: A164886 (base 2), A164996 (base 3), A165035 (base 5), A165054 (base 6), A165074 (base 7), A165093 (base 8), A165113 (base 9), A151963 (base 10).

A165035 (Length of preperiodic part) + (length of cycle) of trajectory of n under iteration of the base-5 Kaprekar map in A165032.

Original entry on oeis.org

1, 2, 2, 2, 2, 3, 2, 3, 1, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 3, 3, 2, 3, 2, 3, 3, 3, 3, 4, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 2, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 4, 3, 2, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 4, 3, 3, 3, 3, 4, 4, 4, 4, 4

Offset: 0

Joseph Myers, Sep 04 2009

Joseph Myers, Table of n, a(n) for n=0..3125
Index entries for the Kaprekar map

Cf. A165032, A165034.

In other bases: A164886 (base 2), A164996 (base 3), A165015 (base 4), A165054 (base 6), A165074 (base 7), A165093 (base 8), A165113 (base 9), A151963 (base 10).

A165054 (Length of preperiodic part) + (length of cycle) of trajectory of n under iteration of the base-6 Kaprekar map in A165051.

Original entry on oeis.org

1, 2, 2, 2, 2, 2, 3, 2, 3, 5, 4, 4, 5, 3, 2, 3, 5, 4, 4, 5, 3, 2, 3, 5, 4, 4, 5, 3, 2, 3, 5, 4, 4, 5, 3, 2, 3, 3, 4, 2, 3, 4, 3, 2, 3, 4, 2, 3, 4, 3, 3, 4, 2, 3, 2, 4, 4, 4, 2, 3, 3, 2, 2, 2, 2, 3, 4, 3, 3, 3, 3, 3, 4, 4, 4, 2, 3, 4, 4, 3, 3, 4, 2, 3, 4, 3, 2, 3, 4, 2, 2, 4, 3, 3, 4, 2, 3, 2, 4, 4, 4, 2, 4, 3, 2

Offset: 0

Joseph Myers, Sep 04 2009

Joseph Myers, Table of n, a(n) for n=0..1296
Index entries for the Kaprekar map

Cf. A165051, A165053.

In other bases: A164886 (base 2), A164996 (base 3), A165015 (base 4), A165035 (base 5), A165074 (base 7), A165093 (base 8), A165113 (base 9), A151963 (base 10).

A165074 (Length of preperiodic part) + (length of cycle) of trajectory of n under iteration of the base-7 Kaprekar map in A165071.

Original entry on oeis.org

1, 2, 2, 2, 2, 2, 2, 3, 2, 3, 4, 5, 3, 5, 4, 3, 2, 3, 4, 5, 3, 5, 4, 3, 2, 3, 4, 5, 3, 5, 4, 3, 2, 3, 4, 5, 3, 5, 4, 3, 2, 3, 4, 5, 3, 5, 4, 3, 2, 3, 3, 5, 3, 3, 4, 5, 3, 2, 3, 5, 3, 3, 4, 5, 3, 3, 5, 3, 3, 4, 3, 5, 5, 5, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 4, 3, 3, 3, 3, 3, 4, 5, 4, 4, 4, 4, 4, 4, 5, 5, 5, 3, 3, 4, 5

Offset: 0

Joseph Myers, Sep 04 2009

Joseph Myers, Table of n, a(n) for n=0..2401
Index entries for the Kaprekar map

Cf. A165071, A165073.

In other bases: A164886 (base 2), A164996 (base 3), A165015 (base 4), A165035 (base 5), A165054 (base 6), A165093 (base 8), A165113 (base 9), A151963 (base 10).

A165092 Length of preperiodic part of trajectory of n under iteration of the base-8 Kaprekar map in A165090.

Original entry on oeis.org

0, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 4, 1, 3, 3, 2, 4, 2, 1, 2, 4, 0, 3, 3, 1, 4, 2, 1, 2, 4, 1, 3, 3, 1, 4, 2, 1, 2, 4, 1, 3, 3, 1, 4, 2, 1, 2, 4, 2, 3, 3, 1, 4, 2, 1, 2, 4, 2, 3, 3, 1, 4, 2, 1, 2, 2, 4, 3, 1, 2, 3, 4, 2, 1, 2, 4, 3, 1, 2, 3, 4, 2, 2, 4, 3, 1, 2, 3, 3, 4, 4, 4, 3, 1, 2, 3, 1, 3, 3, 3, 3, 1, 2, 3, 2

Offset: 0

Joseph Myers, Sep 04 2009

Joseph Myers, Table of n, a(n) for n=0..4096
Index entries for the Kaprekar map

Cf. A165090, A165093.

In other bases: A164885 (base 2), A164995 (base 3), A165014 (base 4), A165034 (base 5), A165053 (base 6), A165073 (base 7), A165112 (base 9), A151962 (base 10).

A165113 (Length of preperiodic part) + (length of cycle) of trajectory of n under iteration of the base-9 Kaprekar map in A165110.

Original entry on oeis.org

1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 3, 3, 5, 4, 3, 2, 5, 3, 3, 2, 3, 3, 5, 4, 3, 3, 5, 3, 3, 2, 3, 3, 5, 4, 3, 4, 5, 3, 3, 2, 3, 3, 5, 4, 3, 4, 5, 2, 3, 2, 3, 3, 5, 3, 3, 4, 5, 3, 3, 2, 3, 3, 5, 3, 3, 4, 5, 3, 3, 2, 3, 4, 5, 3, 3, 4, 5, 3, 3, 2, 3, 3, 6, 5, 3, 3, 4, 5, 6, 3, 2, 3, 6, 5, 3, 3, 4, 5, 6, 3, 3, 6, 5, 3

Offset: 0

Joseph Myers, Sep 04 2009

Joseph Myers, Table of n, a(n) for n=0..6561
Index entries for the Kaprekar map

Cf. A165110, A165112.

In other bases: A164886 (base 2), A164996 (base 3), A165015 (base 4), A165035 (base 5), A165054 (base 6), A165074 (base 7), A165093 (base 8), A151963 (base 10).

cp's OEIS Frontend

A164886 (Length of preperiodic part) + (length of cycle) of trajectory of n under iteration of the base-2 Kaprekar map in A164884.

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A151963 (Length of preperiodic part) + (length of cycle) of trajectory of n under iteration of the Kaprekar map in A151949.

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Maple

Mathematica

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A164996 (Length of preperiodic part) + (length of cycle) of trajectory of n under iteration of the base-3 Kaprekar map in A164993.

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A165015 (Length of preperiodic part) + (length of cycle) of trajectory of n under iteration of the base-4 Kaprekar map in A165012.

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A165035 (Length of preperiodic part) + (length of cycle) of trajectory of n under iteration of the base-5 Kaprekar map in A165032.

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A165054 (Length of preperiodic part) + (length of cycle) of trajectory of n under iteration of the base-6 Kaprekar map in A165051.

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A165074 (Length of preperiodic part) + (length of cycle) of trajectory of n under iteration of the base-7 Kaprekar map in A165071.

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A165092 Length of preperiodic part of trajectory of n under iteration of the base-8 Kaprekar map in A165090.

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A165113 (Length of preperiodic part) + (length of cycle) of trajectory of n under iteration of the base-9 Kaprekar map in A165110.

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