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%I #9 Feb 13 2017 21:08:58
%S 1,2,3,4,5,6,7,8,9,11,88,111,232,535,575,646,686,818,838,1111,2132,
%T 2312,2472,2692,2742,2962,5135,5175,5315,5715,5795,5975,6146,6186,
%U 6226,6246,6416,6426,6696,6776,6816,6966,8118,8138,8278,8318,8728,11111
%N Numbers beginning and ending with their multiplicative digital root.
%C If NA(1)A(2)...A(j)N is MDR strong then also Na(1)a(2)...a(j)N is MDR strong where a(1)a(2)...a(j) is any permutation of A(1)A(2)...A(j) and if any of A(1),A(2),...,A(j) say A(1) is composite then also NB(1)...B(k)A(2)...A(j) is MDR strong where A(1)=B(1)*B(2)*...*B(k), so MDR strong numbers with greater number of digits are likely to be more frequent.
%H Harvey P. Dale, <a href="/A064704/b064704.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Ar#10-automatic">Index entries for 10-automatic sequences</a>.
%t dr[n_]:=NestWhile[Times@@IntegerDigits[#]&,n,#>9&];bemdrQ[n_]:=Module[ {idn=IntegerDigits[n]},First[idn]==Last[idn]==dr[n]]; Select[Range[ 12000], bemdrQ] (* _Harvey P. Dale_, Oct 21 2011 *)
%Y Cf. A031347.
%K nonn,base,easy
%O 1,2
%A _Santi Spadaro_, Oct 13 2001
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