A108192 Numbers k such that k and the product of the digits of k have at least one digit in common.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 26, 30, 31, 35, 40, 41, 46, 50, 51, 53, 55, 57, 59, 60, 61, 62, 64, 66, 68, 70, 71, 75, 80, 81, 86, 90, 91, 95, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116

Offset

1,3

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Example

Product of digits of 26 is 12 (2*6=12); "26" and "12" share the digit "2".

Mathematica

Select[Range[0, 116], Length[Intersection[IntegerDigits[#], IntegerDigits[Apply[Times, IntegerDigits[#]]]]]>0&]  (* James C. McMahon, Feb 25 2024 *)

Prog

(Python)
from math import prod
def ok(n): return set(s:=str(n)) & set(str(prod(map(int, s)))) != set()
print([k for k in range(117) if ok(k)]) # Michael S. Branicky, Feb 25 2024

Crossrefs

Cf. A007954.

Sequence in context: A246101 A241673 A258009 * A250395 A371123 A273880

Adjacent sequences: A108189 A108190 A108191 * A108193 A108194 A108195

Keyword

base,easy,nonn

Author

Eric Angelini, Jun 15 2005

Status

approved