A151957 -id:A151957 - cp's OEIS frontend

A151958 Length of cycle mentioned in A151957.

1, 1, 1, 4, 7, 8, 3, 14, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 3, 5, 3, 3, 3, 3, 3, 3, 3, 3, 5, 1, 3, 3, 3, 3, 3, 3, 1, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 5, 5, 5, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3

Offset: 2

Harvey P. Dale and N. J. A. Sloane, Aug 18 2009

Joseph Myers, Table of n, a(n) for n=2..1000 [From _Joseph Myers_, Aug 21 2009]
Index entries for the Kaprekar map

A151967 Iterate the Kaprekar map of A151949 starting at the n-digit number 100...01; sequence gives the lowest number in the resulting cycle.

Original entry on oeis.org

0, 0, 6174, 62964, 420876, 7509843, 64308654, 864197532, 6431088654, 86420987532, 643310886654, 8643209876532, 43333208766666, 885432098765412, 6543331088666544, 88754320987654212, 643111110888888654

Offset: 2

N. J. A. Sloane, Aug 20 2009

			a(6) = 420876: 100001 -> 109989 -> 980811 -> 976221 -> 853542 -> 620874 -> 851742 -> 750843 -> 840852 -> 860832 -> 862632 -> 642654 -> 420876 -> 851742 -> ..., a cycle of length 7 with smallest member 420876.

Joseph Myers, Table of n, a(n) for n=2..1000 [From _Joseph Myers_, Aug 21 2009]
Index entries for the Kaprekar map

See A151968 for the length of the cycles. Cf. A151957, A151958.

Different from A151957.

(Mma program from Harvey P. Dale) To find the first 20 terms of the trajectory of 10001, for instance:
f[n_]:=Module[{idn=IntegerDigits[n],idns},idns=Sort[idn];Abs[FromDigits[ idns]-FromDigits[Reverse[idns]]]]
NestList[f,10001,20]

Extended by Joseph Myers, Aug 21 2009

A151955 a(1) = 102; thereafter a(n) = (a(n-1) with digits sorted into descending order) - (a(n-1) with digits sorted into ascending order) (see the Kaprekar map, A151949).

Original entry on oeis.org

102, 198, 792, 693, 594, 495, 495, 495, 495, 495, 495, 495, 495, 495, 495, 495, 495, 495, 495, 495, 495, 495, 495, 495, 495, 495, 495, 495, 495, 495, 495, 495, 495, 495, 495, 495, 495, 495, 495, 495, 495, 495, 495, 495, 495, 495, 495, 495

Offset: 1

Harvey P. Dale. Aug 18 2009

102 is the smallest starting value which does not converge to 0.

Converges to the fixed point 495. For the list of fixed points see A099009.

Index entries for the Kaprekar map

Cf. A099009, A151946, A151949, A151947, A151957.

A151956 a(1) = 1002; thereafter a(n) = (a(n-1) with digits sorted into descending order) - (a(n-1) with digits sorted into ascending order) (see the Kaprekar map, A151949).

Original entry on oeis.org

1002, 2088, 8532, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174

Offset: 1

Harvey P. Dale, Aug 18 2009

For the list of fixed points see A099009.

Index entries for the Kaprekar map

Cf. A099009, A151947, A151949, A151950, A069746, A151955, A151951, A151957.

cp's OEIS Frontend

A151958 Length of cycle mentioned in A151957.

Views

Author

Keywords

Links

Crossrefs

Extensions

A151967 Iterate the Kaprekar map of A151949 starting at the n-digit number 100...01; sequence gives the lowest number in the resulting cycle.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

Extensions

A151955 a(1) = 102; thereafter a(n) = (a(n-1) with digits sorted into descending order) - (a(n-1) with digits sorted into ascending order) (see the Kaprekar map, A151949).

Views

Author

Keywords

Comments

Links

Crossrefs

A151956 a(1) = 1002; thereafter a(n) = (a(n-1) with digits sorted into descending order) - (a(n-1) with digits sorted into ascending order) (see the Kaprekar map, A151949).

Views

Author

Keywords

Comments

Links

Crossrefs