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.

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

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..36.

Example

a(13) = 11037, the three spaces around 13 ( -1-3-) are filled with 1,0 and 7.

Crossrefs

Cf. A110734, A110736, A080436.

Sequence in context: A194429 A320121 A084042 * A277622 A101317 A274945

Adjacent sequences: A110732 A110733 A110734 * A110736 A110737 A110738

Keyword

base,easy,nonn

Author

Amarnath Murthy, Aug 09 2005

Extensions

Edited and extended by Franklin T. Adams-Watters, Sep 25 2006

Status

approved