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%I #10 Mar 19 2022 11:09:15
%S 110,120,132,140,150,162,175,184,198,11000,11011,11028,11037,11046,
%T 11055,11168,11271,11088,11096,12000,12012,12122,12236,12048,12050,
%U 12064,12177,12180,12093,13200,13113,13024,13035,13940,13055,13068
%N 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.
%C 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.
%C 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
%e a(13) = 11037, the three spaces around 13 ( -1-3-) are filled with 1,0 and 7.
%Y Cf. A110734, A110736, A080436.
%K base,easy,nonn
%O 1,1
%A _Amarnath Murthy_, Aug 09 2005
%E Edited and extended by _Franklin T. Adams-Watters_, Sep 25 2006