

A277061


Numbers with multiplicative digital root > 0.


3



1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 46, 47, 48, 49, 51, 53, 57, 61, 62, 63, 64, 66, 67, 68, 71, 72, 73, 74, 75, 76, 77, 79, 81, 82, 83, 84, 86, 88, 89, 91, 92, 93, 94, 97, 98, 99, 111, 112
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

Question: when will numbers not in this sequence outnumber numbers in this sequence? Up to n = 1249, there are 524 terms, so 525 terms not in this sequence. Up to n = 1522, there are n/2 terms. No n > 1522 has that property. Up to 10^10, only about 1.46% of numbers are a term.
To find how many terms there are up to 10^n, see if A009994(i) is for 2 <= i <= binomial(n + 9, 9). If it is then that adds A047726(A009994(i)) to the total (we don't have to worry about digits 0 in A009994(i) as there aren't any for the specified i). One may put further constraints on i. For example, A009994(i) can't contain an even digit and a 5 in the same number.  David A. Corneth, Sep 27 2016


LINKS

Table of n, a(n) for n=1..77.
Index entries for 10automatic sequences.


EXAMPLE

25 is not in this sequence because 2*5 = 10 and 1*0 = 0.


MATHEMATICA

Select[Range@ 112, FixedPoint[Times @@ IntegerDigits@ # &, #] > 0 &] (* Michael De Vlieger, Sep 26 2016 *)


PROG

is(n) = n=digits(n); while(#n>1, n=digits(prod(i=1, #n, n[i]))); #n>0 \\ David A. Corneth, Sep 27 2016


CROSSREFS

Cf. A009994, A047726.
Cf. A031347, A034048 (complement).
Cf. A028843 (a subsequence).
Union of A002275, A034049, A034050, A034051, A034052, A034053, A034054, A034055, A034056 (numbers having multiplicative digital roots 19).
Cf. A052382 (a supersequence).
Sequence in context: A020731 A229300 A229301 * A090274 A254621 A227510
Adjacent sequences: A277058 A277059 A277060 * A277062 A277063 A277064


KEYWORD

nonn,base


AUTHOR

J. Lowell, Sep 26 2016


EXTENSIONS

More terms from Michael De Vlieger, Sep 26 2016


STATUS

approved



