A371123 Numbers whose decimal representation contains the digital root of the product of their digits.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 29, 30, 31, 34, 37, 39, 40, 41, 43, 46, 49, 50, 51, 59, 60, 61, 64, 67, 69, 70, 71, 73, 76, 79, 80, 81, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112

Offset

1,3

Comments

All numbers with a 0 digit (A011540) are terms, since their product of digits is 0.

All numbers with a 9 digit (A011539) are terms, since their product of digits is a multiple of 9 and so has digital root 9 if no 0 digits, or 0 if any 0 digit.

Links

Table of n, a(n) for n=1..72.

Example

29 is a term because 2*9=18 and 1+8=9 and 29 contains digit 9.

Mathematica

digRoot[n_] := If[n == 0, 0, Mod[n - 1, 9] + 1]; q[n_] := Module[{d = IntegerDigits[n]}, MemberQ[d, digRoot[Times @@ d]]]; Select[Range[0, 112], q] (* Amiram Eldar, Mar 11 2024 *)

Crossrefs

Cf. A007954, A010888, A011539, A011540, A119246.

Sequence in context: A258009 A108192 A250395 * A273880 A203565 A132263

Adjacent sequences: A371120 A371121 A371122 * A371124 A371125 A371126

Keyword

nonn,base,easy

Author

Saish S. Kambali, Mar 11 2024

Status

approved