A132378 Smallest integer that starts with n and is divisible by every nonzero digit of n.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 132, 140, 15, 162, 175, 184, 198, 20, 210, 22, 234, 24, 250, 264, 2702, 280, 2916, 30, 312, 324, 33, 348, 3510, 36, 378, 384, 396, 40, 412, 420, 432, 44, 4500, 468, 476, 48, 4932, 50, 510, 520, 5310, 540, 55, 5610, 5705, 5800, 5940

Offset

1,2

Comments

Note that a number that starts with n and is divisible by lcm(1, 2, ..., 9) = 2520 always satisfies the conditions. And there is such a number between n0000 and n2519. Therefore a(n) < 10000n + 2520. Hence to find a(n) one needs to check numbers n, n0..n9, n00..n99, n000..n999, n0000..n2519.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

TopCoder problem DivisibleByDigits

Maple

f:= proc(n) local r, d, q ;
   r:= ilcm(op(convert(convert(n, base, 10), set) minus {0, 1}));
   if n mod r = 0 then return n fi;
   for d from 1 do
     q:= -(n*10^d) mod r;
     if q < 10^d then return n*10^d+q fi;
   od
end proc:
map(f, [$1..100]); # Robert Israel, Feb 01 2017

Prog

lcm = lcm(all nonzero digits of n) for (p10 = 1;; p10 *= 10) { for (suffix = 0; suffix < p10; suffix++) { m = n * p10 + suffix; if (m % lcm == 0) return m; } }

Crossrefs

Sequence in context: A004863 A055648 A004874 * A043317 A044914 A004885

Adjacent sequences: A132375 A132376 A132377 * A132379 A132380 A132381

Keyword

base,easy,nonn

Author

Mikhail Dvorkin (mikhail.dvorkin(AT)gmail.com), Nov 10 2007

Status

approved