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A034048 Numbers with multiplicative digital root value 0. 19
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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,base,easy
AUTHOR
Patrick De Geest, Sep 15 1998
STATUS
approved

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Last modified February 26 12:26 EST 2024. Contains 370352 sequences. (Running on oeis4.)