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A099010 Cycle elements of the Kaprekar mapping f(n) = n' - n'', where in n' the digits of n are arranged in descending, in n'' in ascending order. +0
2
53955, 59994, 61974, 62964, 63954, 71973, 74943, 75933, 82962, 83952, 420876, 642654, 750843, 840852, 851742, 860832, 862632, 7509843, 7519743, 7619733, 8429652, 8439552, 8649432, 8719722, 9529641 (list; graph; listen)
OFFSET

1,1

COMMENT

86526432, 64308654, 83208762 form a cycle of length three, and 86308632, 8632663 2, 64326654, 43208766, 85317642, 75308643, 84308652 form a cycle of length seven. It is conjectured that these are the only cycles of eight-digit numbers and that these numbers (sorted) are the next ten terms.

LINKS

Eric Weisstein's World of Mathematics, KaprekarRoutine

EXAMPLE

53955 and 59994 form a cycle of length 2 and hence are terms: 53955 -> 95553 - 35559 = 59994 -> 99954 - 45999 = 53955.

CROSSREFS

Cf. A090429, A069746, A099009.

Sequence in context: A061330 A099231 A100422 this_sequence A038564 A083616 A092008

Adjacent sequences: A099007 A099008 A099009 this_sequence A099011 A099012 A099013

KEYWORD

nonn,base

AUTHOR

Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Sep 22 2004

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Last modified November 21 14:49 EST 2008. Contains 150807 sequences.


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