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.

1, 2, 3, 4, 5, 6, 7, 8, 9, 89, 394, 605, 894, 3944, 6055, 8944, 15111, 84888, 89444, 894444

Offset: 1

Author

Rodolfo Kurchan, May 10 2009, May 11 2009, May 16 2009

Keywords

• base
• fini
• nonn
• full

Comments

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.

The sequence consists of those k where d=b, that is, where these two neighbors are equidistant from k.

From Donovan Johnson, Sep 29 2009: (Start)

15111 has neighbors 9876 and 20346, distance 5235.

84888 has neighbors 79653 and 90123, distance 5235.

89444 has neighbors 76532 and 102356, distance 12912.

894444 has neighbors 765321 and 1023567, distance 129123.

Sequence is complete.

(End)

Examples

			6 has neighbors 5 and 7, common distance 1.
89 has neighbors 76 and 102, common distance 13.
394 has neighbors 287 and 501, distance 107.
605 has neighbors 498 and 712, distance 107.
894 has neighbors 765 and 1023, distance 129.
3944 has neighbors 2876 and 5012, distance 1068.
6055 has neighbors 4987 and 7123, distance 1068.
8944 has neighbors 7653 and 10235, distance 1291.
94 is not in the sequence because 87 and 102 have distances 7 and 8.
		

Links

• Rodolfo Kurchan and Claudio Meller, Snark e-mail list, May 10, 2009 [Dead link]

Extensions

Edited by R. J. Mathar, May 20 2009

a(17)-a(20) from Donovan Johnson, Sep 29 2009