A034048 Numbers with multiplicative digital root value 0.

0, 10, 20, 25, 30, 40, 45, 50, 52, 54, 55, 56, 58, 59, 60, 65, 69, 70, 78, 80, 85, 87, 90, 95, 96, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 120, 125, 130, 140, 145, 150, 152, 154, 155, 156, 158, 159, 160, 165, 169, 170, 178, 180, 185, 187, 190, 195

Offset

1,2

Comments

Numbers with root value 1 are the 'repunits' (see A000042).

This sequence has density 1. - Franklin T. Adams-Watters, Apr 01 2009

Any integer with at least one 0 among its base 10 digits is in this sequence. - Alonso del Arte, Aug 29 2014

This sequence is 10-automatic: it contains numbers with a 0, or with a 5 and any even digit. - Charles R Greathouse IV, Feb 13 2017

Links

Franklin T. Adams-Watters, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Multiplicative Digital Root

Index entries for 10-automatic sequences.

Example

20 is in the sequence because 2 * 0 = 0.
25 is in the sequence because 2 * 5 = 10 and 1 * 0 = 0.

Mathematica

mdr0Q[n_]:=NestWhile[Times@@IntegerDigits[#]&, n, #>9&]==0; Select[Range[ 0, 200], mdr0Q] (* Harvey P. Dale, Jul 21 2020 *)

Prog

(PARI) is(n)=factorback(digits(n))==0 \\ Charles R Greathouse IV, Feb 13 2017

Crossrefs

Cf. A031347, A034048, A002275, A034049, A034050, A034051, A034052, A034053, A034054, A034055, A034056 (numbers having multiplicative digital roots 0-9).

Cf. the subsets A011540 and A008592.

Sequence in context: A364325 A144140 A361337 * A199978 A342142 A179819

Adjacent sequences: A034045 A034046 A034047 * A034049 A034050 A034051

Keyword

nonn,base,easy

Author

Patrick De Geest, Sep 15 1998

Status

approved