A343550 Numbers k > 9 such that the number m formed by inserting a digit 0 between each pair of digits in k is divisible by k.

10, 15, 18, 20, 30, 40, 45, 50, 60, 70, 80, 90, 100, 111, 120, 126, 150, 180, 200, 222, 240, 250, 285, 300, 333, 360, 400, 444, 450, 480, 500, 555, 600, 666, 700, 750, 777, 800, 888, 900, 999, 1000, 1041, 1110, 1185, 1200, 1260, 1395, 1443, 1500, 1554, 1665

Offset: 1

Author

Lars Blomberg, Apr 19 2021

Keywords

• nonn
• base

Comments

One-digit terms are not considered since no 0 digits can be inserted.

If k is a term then so is k*10^i, i > 0.

If k is a term then so is k*i, 2 <= i <= 9 as long as no carry occurs in the multiplication.

The number of terms with n digits is (12, 29, 51, 107, 149, 240, 308, 438, 566, 789, 1007), 2 <= n <= 12.

Examples

			18 is a term because 108/18=6, and so is 1185 because 1010805/1185=853.
10101/111=91, 1010100/1110=910, 101010000/11100=9100, ... so 111, 1110, 11100, ... are all terms.
1000401/1041=961 and 2000802/2082=961 so 1041 and 2082 are terms but 3123 is not since it does not divide 3010203.
		

Crossrefs

Cf. A051022, A285176, A343551, A343552.

Cf. A062846 (binary), A062891 (ternary).