A064704 Numbers beginning and ending with their multiplicative digital root.

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.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Index entries for 10-automatic sequences.

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

Adjacent sequences: A064701 A064702 A064703 * A064705 A064706 A064707

Keyword

nonn,base,easy

Author

Santi Spadaro, Oct 13 2001

Status

approved