A123895 Restricted growth string for the (decimal expansion of the) number n.

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

Offset: 0

Author

N. J. A. Sloane, Nov 20 2006

Keywords

• nonn
• base

Comments

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.

Examples

			To find a(66041171): 066041171 -> 011023343 -> 11023343.
		

References

• D. E. Knuth, The Art of Computer Programming, vol. 4A, Combinatorial Algorithms, Section 7.2.1.5, p. 432, Problems 4 and 5.

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A123896, A123902.

Programs

Maple

read("transforms"):
A123895 := proc(n)
    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:
seq(A123895(n),n=0..60) ; # R. J. Mathar, Dec 09 2015

Mathematica

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 *)

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
' Franklin T. Adams-Watters