A034050 Numbers with multiplicative digital root value 3.

3, 13, 31, 113, 131, 311, 1113, 1131, 1311, 3111, 11113, 11131, 11311, 13111, 31111, 111113, 111131, 111311, 113111, 131111, 311111, 1111113, 1111131, 1111311, 1113111, 1131111, 1311111, 3111111, 11111113, 11111131, 11111311, 11113111

Offset: 1

Author

Patrick De Geest, Sep 15 1998

Keywords

• nonn
• base
• easy

Comments

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

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• 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

Maple

seq(seq((10^m-1)/9 + 2*10^j,j=0..m-1),m=1..10); # Robert Israel, Sep 27 2016

Mathematica

Sort[Flatten[Table[FromDigits/@Permutations[Join[{3},PadRight[{},n,1]]],{n,0,8}]]] (* Harvey P. Dale, Jul 16 2012 *)

Python

# through 8-digit terms
print([int("1"*(d-i)+"3"+"1"*i) for d in range(8) for i in range(d+1)]) # Michael S. Branicky, Mar 13 2021

Formula

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

a(m*(m-1)/2+j+1) = (10^m-1)/9 + 2*10^j for 0 <= j < m. - Robert Israel, Sep 27 2016