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

Author

Santi Spadaro, Oct 13 2001

Keywords

• nonn
• base
• easy

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.

Crossrefs

Cf. A031347.

Programs

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 *)