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A160343 Numbers k such that the two closest numbers above and below k, which are in A010784 and which have no common digit with k, have the same distance to k.

%I A160343 #16 Jan 01 2022 09:53:12
%S A160343 1,2,3,4,5,6,7,8,9,89,394,605,894,3944,6055,8944,15111,84888,89444,
%T A160343 894444
%N A160343 Numbers k such that the two closest numbers above and below k, which are in A010784 and which have no common digit with k, have the same distance to k.
%C A160343 For each integer k, define the smallest upper neighbor k+d with d > 0 such that k+d contains each digit at most once (see A010784) and has none of the digits of k. Define also the largest lower neighbor k-b with b > 0 such that k-b contains each digit at most once and has none of the digits of k.
%C A160343 The sequence consists of those k where d=b, that is, where these two neighbors are equidistant from k.
%C A160343 From _Donovan Johnson_, Sep 29 2009: (Start)
%C A160343 15111 has neighbors 9876 and 20346, distance 5235.
%C A160343 84888 has neighbors 79653 and 90123, distance 5235.
%C A160343 89444 has neighbors 76532 and 102356, distance 12912.
%C A160343 894444 has neighbors 765321 and 1023567, distance 129123.
%C A160343 Sequence is complete.
%C A160343 (End)
%H A160343 Rodolfo Kurchan and Claudio Meller, <a href="http://mathforum.org/kb/message.jspa?messageID=6704132&amp;tstart=0">Snark e-mail list, May 10, 2009</a> [Dead link]
%e A160343 6 has neighbors 5 and 7, common distance 1.
%e A160343 89 has neighbors 76 and 102, common distance 13.
%e A160343 394 has neighbors 287 and 501, distance 107.
%e A160343 605 has neighbors 498 and 712, distance 107.
%e A160343 894 has neighbors 765 and 1023, distance 129.
%e A160343 3944 has neighbors 2876 and 5012, distance 1068.
%e A160343 6055 has neighbors 4987 and 7123, distance 1068.
%e A160343 8944 has neighbors 7653 and 10235, distance 1291.
%e A160343 94 is not in the sequence because 87 and 102 have distances 7 and 8.
%K A160343 base,fini,nonn,full
%O A160343 1,2
%A A160343 _Rodolfo Kurchan_, May 10 2009, May 11 2009, May 16 2009
%E A160343 Edited by _R. J. Mathar_, May 20 2009
%E A160343 a(17)-a(20) from _Donovan Johnson_, Sep 29 2009