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A132378 Smallest integer that starts with n and is divisible by every nonzero digit of n. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 24 12:49 EST 2022. Contains 350538 sequences. (Running on oeis4.)