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

1,1

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.

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

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 *)

Prog

(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

Crossrefs

Cf. A031347.

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

Sequence in context: A058264 A242905 A213970 * A107689 A339945 A154834

Adjacent sequences: A034047 A034048 A034049 * A034051 A034052 A034053

Keyword

nonn,base,easy

Author

Patrick De Geest, Sep 15 1998

Status

approved