A034056 Numbers with multiplicative digital root value 9.

9, 19, 33, 91, 119, 133, 191, 313, 331, 911, 1119, 1133, 1191, 1313, 1331, 1911, 3113, 3131, 3311, 9111, 11119, 11133, 11191, 11313, 11331, 11911, 13113, 13131, 13311, 19111, 31113, 31131, 31311, 33111, 91111, 111119, 111133, 111191, 111313, 111331

Offset: 1

Author

Patrick De Geest, Sep 15 1998

Keywords

• nonn
• base
• easy

Comments

Numbers with one 9 or two 3s, and zero or more 1s. - Daniel Forgues, Oct 09 2011

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Multiplicative Digital Root
• Index entries for 10-automatic sequences.

Crossrefs

Cf. A031347.

Cf. A034048, A002275, A034049, A034050, A034051, A034052, A034053, A034054, A034055, A034056 (numbers having multiplicative digital roots 0-9).

Programs

Mathematica

Module[{nn=6,ne,te},ne=Union[FromDigits/@Flatten[Permutations/@Table[PadRight[{9},n,1],{n,nn}],1]];te=Rest[Union[FromDigits/@ Flatten[ Permutations/@Table[PadRight[{3,3},n,1],{n,nn}],1]]];Join[ne,te]]//Sort (* Harvey P. Dale, Apr 14 2025 *)

Formula

There are n(n+1)(n+2)/6 elements up to 10^n, so a(n) is about 10^sqrt(6n).