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Search: id:A096085
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| A096085 |
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a(n) is the least positive integer such that for 1 <= k <= n, the concatenation of the k terms a(n-k+1) through a(n) is a multiple of k. |
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+0
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| 1, 2, 6, 4, 20, 60, 340, 920, 600, 1000, 14240, 31560, 100120, 140960, 315960, 314800, 7523840, 1020480, 109764640, 66757520, 23256960, 2200720, 1260893360, 1059221040, 16184204800, 34159566800, 18162880800, 68345405200
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OFFSET
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1,2
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COMMENT
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It suffices to check this for prime-power values of k. To see this, let k = a*b, where a and b are relatively prime. The concatenation of k terms can be viewed as a concatenation of a numbers, each of which is the concatenation of b terms. The first a-1 of these were previously chosen to be multiples of b, so if the last is also a multiple of b, then the concatenation of all k terms is a multiple of b. By the same argument, the concatenation of all k terms is a multiple of a, and since a and b are relatively prime, it is a multiple of k. - David Wasserman (dwasserm(AT)earthlink.net), May 21 2007
a(n) exists for all n, because the Chinese Remainder Theorem shows that a d-digit solution must exist if 9*10^(d-1) >= A003418(n). - David Wasserman (dwasserm(AT)earthlink.net), May 21 2007
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EXAMPLE
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12, 26, 64, and 420 are multiples of 2.
126, 264, 6420, and 42060 are multiples of 3.
1264, 26420, 642060, and 42060340 are multiples of 4.
126420, 2642060, 642060340, and 42060340920 are multiples of
5.
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CROSSREFS
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Adjacent sequences: A096082 A096083 A096084 this_sequence A096086 A096087 A096088
Sequence in context: A075435 A069875 A019088 this_sequence A106831 A038212 A039656
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KEYWORD
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base,nonn,less
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jun 22 2004
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EXTENSIONS
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Edited and extended by David Wasserman (dwasserm(AT)earthlink.net), May 21 2007
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