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A123895
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Restricted growth string for the (decimal expansion of the) number n.
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4
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0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 10, 11, 12, 12, 12, 12, 12, 12, 12, 12, 10, 12, 11, 12, 12, 12, 12, 12, 12, 12, 10, 12, 12, 11, 12, 12, 12, 12, 12, 12, 10, 12, 12, 12, 11, 12, 12, 12, 12, 12, 10, 12, 12, 12, 12, 11, 12, 12, 12, 12, 10, 12, 12, 12, 12, 12, 11, 12, 12
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,11
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COMMENTS
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Write n in base 10 prefixed with a 0. Read this string from left to right. Write a 0 each time you see the first distinct digit (which is 0), write a 1 each time you see the second distinct digit, write a 2 each time you see the third distinct digit and so on. Finally, delete the leading 0's.
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REFERENCES
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D. E. Knuth, The Art of Computer Programming, vol. 4A, Combinatorial Algorithms, Section 7.2.1.5, p. 432, Problems 4 and 5.
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LINKS
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EXAMPLE
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To find a(66041171): 066041171 -> 011023343 -> 11023343.
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MAPLE
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read("transforms"):
local dgs, Lmap, idx, dig, pos, Lredu ;
dgs := [op(convert(n, base, 10)) , 0];
Lmap := [] ;
for idx from -1 to -nops(dgs) by -1 do
dig := op(idx, dgs) ;
if not member(dig, Lmap) then
Lmap := [op(Lmap), dig] ;
end if;
end do:
Lredu := [] ;
for idx from -1 to -nops(dgs) by -1 do
member(op(idx, dgs), Lmap, 'pos') ;
Lredu := [op(Lredu), pos-1] ;
end do:
digcatL(Lredu) ;
end proc:
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MATHEMATICA
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f[n_] := Block[{d = Prepend[IntegerDigits@ n, 0], a, b, w}, b = DeleteDuplicates@ d; a = Range[0, Length@ b]; w = FromDigits@ Flatten[Part[a, FirstPosition[b, #]] & /@ d]; w]; Table[f@ n, {n, 0, 67}] (* Michael De Vlieger, Dec 09 2015, Version 10 *)
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PROG
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(VBA)
Public Function RestrictedGrowthString(ByVal x As String) As String
Dim i As Long
Dim dig As Integer
Dim pos As Long
For i = 1 To Len(x)
If Mid(x, i, 1) = "0" Then
RestrictedGrowthString = RestrictedGrowthString & "0"
Else
pos = InStr(x, Mid(x, i, 1))
If pos = i Then
dig = dig + 1
RestrictedGrowthString = RestrictedGrowthString &
Format(dig)
Else
RestrictedGrowthString = RestrictedGrowthString &
Mid(RestrictedGrowthString, pos, 1)
End If
End If
Next i
End Function
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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