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
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
(PARI) 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
KEYWORD
nonn,base
AUTHOR
J. Lowell, Sep 26 2016
EXTENSIONS
More terms from Michael De Vlieger, Sep 26 2016
STATUS
approved