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A277061
Numbers with multiplicative digital root > 0.
4
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, 113, 114, 115
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
Cf. A031347, A034048 (complement).
Cf. A028843 (a subsequence).
Union of A002275, A034049, A034050, A034051, A034052, A034053, A034054, A034055, A034056 (numbers having multiplicative digital roots 1-9).
Cf. A052382 (a supersequence).
Sequence in context: A020731 A229300 A229301 * A361978 A090274 A254621
KEYWORD
nonn,base
AUTHOR
J. Lowell, Sep 26 2016
EXTENSIONS
More terms from Michael De Vlieger, Sep 26 2016
STATUS
approved