A343550 - OEIS

%I #16 Apr 20 2021 10:27:22

%S 10,15,18,20,30,40,45,50,60,70,80,90,100,111,120,126,150,180,200,222,

%T 240,250,285,300,333,360,400,444,450,480,500,555,600,666,700,750,777,

%U 800,888,900,999,1000,1041,1110,1185,1200,1260,1395,1443,1500,1554,1665

%N 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.

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

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

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

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

%e 18 is a term because 108/18=6, and so is 1185 because 1010805/1185=853.

%e 10101/111=91, 1010100/1110=910, 101010000/11100=9100, ... so 111, 1110, 11100, ... are all terms.

%e 1000401/1041=961 and 2000802/2082=961 so 1041 and 2082 are terms but 3123 is not since it does not divide 3010203.

%Y Cf. A051022, A285176, A343551, A343552.

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

%K nonn,base

%O 1,1

%A _Lars Blomberg_, Apr 19 2021