

A110735


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.


3



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

1,1


COMMENTS

Conjecture: no term is zero. For a kdigit 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. AdamsWatters, Sep 25 2006


LINKS



EXAMPLE

a(13) = 11037, the three spaces around 13 ( 13) are filled with 1,0 and 7.


CROSSREFS



KEYWORD

base,easy,nonn


AUTHOR



EXTENSIONS



STATUS

approved



