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

%I A123895 #27 Jul 24 2021 01:13:33
%S A123895 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,
%T A123895 12,12,12,12,10,12,12,11,12,12,12,12,12,12,10,12,12,12,11,12,12,12,12,
%U A123895 12,10,12,12,12,12,11,12,12,12,12,10,12,12,12,12,12,11,12,12
%N A123895 Restricted growth string for the (decimal expansion of the) number n.
%C A123895 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.
%D A123895 D. E. Knuth, The Art of Computer Programming, vol. 4A, Combinatorial Algorithms, Section 7.2.1.5, p. 432, Problems 4 and 5.
%H A123895 Michael De Vlieger, <a href="/A123895/b123895.txt">Table of n, a(n) for n = 0..10000</a>
%e A123895 To find a(66041171): 066041171 -> 011023343 -> 11023343.
%p A123895 read("transforms"):
%p A123895 A123895 := proc(n)
%p A123895     local dgs,Lmap,idx,dig,pos,Lredu ;
%p A123895     dgs := [op(convert(n,base,10)) ,0];
%p A123895     Lmap := [] ;
%p A123895     for idx from -1 to -nops(dgs) by -1 do
%p A123895         dig := op(idx,dgs) ;
%p A123895         if not member(dig,Lmap) then
%p A123895             Lmap := [op(Lmap),dig] ;
%p A123895         end if;
%p A123895     end do:
%p A123895     Lredu := [] ;
%p A123895     for idx from -1 to -nops(dgs) by -1 do
%p A123895         member(op(idx,dgs),Lmap,'pos') ;
%p A123895         Lredu := [op(Lredu),pos-1] ;
%p A123895     end do:
%p A123895     digcatL(Lredu) ;
%p A123895 end proc:
%p A123895 seq(A123895(n),n=0..60) ; # _R. J. Mathar_, Dec 09 2015
%t A123895 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 *)
%o A123895 (VBA)
%o A123895 Public Function RestrictedGrowthString(ByVal x As String) As String
%o A123895   Dim i As Long
%o A123895   Dim dig As Integer
%o A123895   Dim pos As Long
%o A123895   For i = 1 To Len(x)
%o A123895     If Mid(x, i, 1) = "0" Then
%o A123895       RestrictedGrowthString = RestrictedGrowthString & "0"
%o A123895     Else
%o A123895       pos = InStr(x, Mid(x, i, 1))
%o A123895       If pos = i Then
%o A123895         dig = dig + 1
%o A123895         RestrictedGrowthString = RestrictedGrowthString &
%o A123895         Format(dig)
%o A123895       Else
%o A123895         RestrictedGrowthString = RestrictedGrowthString &
%o A123895         Mid(RestrictedGrowthString, pos, 1)
%o A123895       End If
%o A123895     End If
%o A123895   Next i
%o A123895 End Function
%o A123895 ' _Franklin T. Adams-Watters_
%Y A123895 Cf. A123896, A123902.
%K A123895 nonn,base
%O A123895 0,11
%A A123895 _N. J. A. Sloane_, Nov 20 2006