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A110735
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Let n = a_1a_2...a_k, where the a_i are digits. a(n) = least multiple of n of the type b_1a_1b_2a_2...a_kb_{k+1}, obtained by inserting single digits b_i in the gaps and both ends; 0 if no such number exists.
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3
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110, 120, 132, 140, 150, 162, 175, 184, 198, 11000, 11011, 11028, 11037, 11046, 11055, 11168, 11271, 11088, 11096, 12000, 12012, 12122, 12236, 12048, 12050, 12064, 12177, 12180, 12093, 13200, 13113, 13024, 13035, 13940, 13055, 13068
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OFFSET
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1,1
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COMMENTS
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Conjecture: no term is zero. For a k-digit number there are k+1 spaces and 10^(k+1) candidates, so the chances that one of them is a multiple of n increases with k on the one hand although the probability decreases because n becomes large.
It may well be the case that no term is zero, but the probabilistic argument above is not sufficient to establish it. It would imply that the probability of a zero is between e^-9 and e^-0.9 (see A110734 - exponents are -9 and -0.9 instead of -10 and -1 because leading digit cannot be zero). For n < 100, the largest term is a(67) = 56079; second largest is a(98) = 29988. - Franklin T. Adams-Watters, Sep 25 2006
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LINKS
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EXAMPLE
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a(13) = 11037, the three spaces around 13 ( -1-3-) are filled with 1,0 and 7.
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CROSSREFS
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KEYWORD
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base,easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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