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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. 1

%I #8 Apr 01 2017 08:39:51

%S 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 621,31,72,41,213,42,53,26,47,58,94,63,171,38,19,12,35,27,36,85,14,

%U 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 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 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 Lars Blomberg, <a href="/A284651/b284651.txt">Table of n, a(n) for n = 1..10000</a>

%e 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 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 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 nonn,base

%O 1,2

%A _Lars Blomberg_ and _Eric Angelini_, Mar 31 2017

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Last modified March 28 11:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)