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Search: id:A132378
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| A132378 |
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Smallest integer that starts with n and is divisible by every nonzero digit of n. |
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+0
1
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| 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; listen)
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OFFSET
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1,2
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COMMENT
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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.
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LINKS
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TopCoder problem DivisibleByDigits
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PROGRAM
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lcm = lcm(all non-zero digits of n) for (p10 = 1; ; p10 *= 10) { for (suffix = 0; suffix < p10; suffix++) { m = n * p10 + suffix; if (m % lcm == 0) return m; } }
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CROSSREFS
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Sequence in context: A004863 A055648 A004874 this_sequence A043317 A044914 A004885
Adjacent sequences: A132375 A132376 A132377 this_sequence A132379 A132380 A132381
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KEYWORD
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base,easy,nonn
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AUTHOR
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Mikhail Dvorkin (mikhail.dvorkin(AT)gmail.com), Nov 10 2007
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