A277061 Numbers with multiplicative digital root > 0.

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

Links

Table of n, a(n) for n=1..80.

Index entries for 10-automatic 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

(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. 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 1-9).

Cf. A052382 (a supersequence).

Sequence in context: A020731 A229300 A229301 * A361978 A090274 A254621

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