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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.
3
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.
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. A062846 (binary), A062891 (ternary).
Sequence in context: A269985 A282648 A139540 * A285176 A135363 A118717
KEYWORD
nonn,base
AUTHOR
Lars Blomberg, Apr 19 2021
STATUS
approved