login
A064704
Numbers beginning and ending with their multiplicative digital root.
1
1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 88, 111, 232, 535, 575, 646, 686, 818, 838, 1111, 2132, 2312, 2472, 2692, 2742, 2962, 5135, 5175, 5315, 5715, 5795, 5975, 6146, 6186, 6226, 6246, 6416, 6426, 6696, 6776, 6816, 6966, 8118, 8138, 8278, 8318, 8728, 11111
OFFSET
1,2
COMMENTS
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.
MATHEMATICA
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 *)
CROSSREFS
Cf. A031347.
Sequence in context: A167152 A246008 A344823 * A083136 A369127 A229623
KEYWORD
nonn,base,easy
AUTHOR
Santi Spadaro, Oct 13 2001
STATUS
approved