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

1,1

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.

Links

Table of n, a(n) for n=1..52.

Example

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).

Sequence in context: A269985 A282648 A139540 * A285176 A135363 A118717

Adjacent sequences: A343547 A343548 A343549 * A343551 A343552 A343553

Keyword

nonn,base

Author

Lars Blomberg, Apr 19 2021

Status

approved