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Search: id:A151957
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| A151957 |
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Iterate the Kaprekar map of A151949 starting at the n-digit number 100...02; sequence gives the lowest number in the resulting cycle. |
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5
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| 0, 495, 6174, 62964, 420876, 7509843, 64308654, 753098643, 6431088654, 86420987532, 643330866654, 8764209875322, 64333308666654, 885432098765412, 6543331088666544, 88543320987665412, 975533110888664421
(list; graph; listen)
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OFFSET
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2,2
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LINKS
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Joseph Myers, Table of n, a(n) for n=2..1000 [From Joseph Myers (jsm(AT)polyomino.org.uk), Aug 21 2009]
Index entries for the Kaprekar map
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MAPLE
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Maple program from R. J. Mathar, Aug 20 2009
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:
A151957 := proc(n)
local tra, x ;
x := 10^(n-1)+2 ;
tra := [x] ;
while true do
x := A151949(x) ;
if member(x, tra, 'l') then
op(l..nops(tra), tra) ;
RETURN(min(%)) ;
fi;
tra := [op(tra), x] :
od:
end:
seq(A151957(n), n=2..60) ;
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MATHEMATICA
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To find the first 20 terms of the trajectory of 10002, for instance:
f[n_]:=Module[{idn=IntegerDigits[n], idns}, idns=Sort[idn]; Abs[FromDigits[ idns]-FromDigits[Reverse[idns]]]]
NestList[f, 10002, 20]
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CROSSREFS
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See A151958 for the length of the cycles. Cf. A151949, A151955 (the trajectory of 102), A151956 (the trajectory of 1002).
See also A151967, A151968.
Sequence in context: A164716 A164718 A151965 this_sequence A099009 A055160 A055157
Adjacent sequences: A151954 A151955 A151956 this_sequence A151958 A151959 A151960
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KEYWORD
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nonn,base
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AUTHOR
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Harvey P. Dale (hpd1(AT)nyu.edu) and N. J. A. Sloane (njas(AT)research.att.com), Aug 18 2009, Aug 19 2009
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EXTENSIONS
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Extended by R. J. Mathar and Joseph Myers (jsm(AT)polyomino.org.uk), Aug 20 2009
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