cp's OEIS Frontend

A284651 Lexicographically earliest sequence of unique numbers such that for each digit "d" exactly one of the gaps to the neighboring digits "d" is equal to d, and no gap is smaller than d.

%I A284651 #8 Apr 01 2017 08:39:51
%S A284651 1,2,13,24,5,3,6,7,4,8,52,9,62,73,18,132,91,21,34,25,32,46,15,17,23,
%T A284651 621,31,72,41,213,42,53,26,47,58,94,63,171,38,19,12,35,27,36,85,14,
%U A284651 176,248,29,51,71,265,28,97,16,100,48,37,54,39,625,724,86,294,200,78,45,161,475,92,61,214,57,89,415,137,68,300
%N A284651 Lexicographically earliest sequence of unique numbers such that for each digit "d" exactly one of the gaps to the neighboring digits "d" is equal to d, and no gap is smaller than d.
%C A284651 The sequence is started with a(1) = 1 and always extended with the smallest integer not yet present and not leading to a contradiction. This sequence is a variant of A284516 and the variant is explained in the "Example" section.
%H A284651 Lars Blomberg, <a href="/A284651/b284651.txt">Table of n, a(n) for n = 1..10000</a>
%e A284651 The first 16 terms of this variant are 1, 2, 13, 24, 5, 3, 6, 7, 4, 8, 52, 9, 62, 73, 18, 132.
%e A284651 The first 16 terms of the orig seq are 1, 2, 13, 24, 5, 3, 6, 7, 4, 8, 52, 9, 62, 73, 18, 131.
%e A284651 The difference is in the last digit of the last term (131 becomes here 132): in the original sequence the first digit "1" of the term "131" is twice at a gap of 1 digit from another "1" (there is indeed a gap of 1 digit between the first "1" of "131" and the "1" of "18" AND there is also a gap of 1 digit between the first and the second "1" of "131"). This is forbidden in this variant, whatever digit "d" you pick: if your digit "d" is at a gap of d from another "d", it cannot be at the same gap of another "d".
%K A284651 nonn,base
%O A284651 1,2
%A A284651 _Lars Blomberg_ and _Eric Angelini_, Mar 31 2017