|
%I #16 Aug 26 2018 01:09:03
%S 0,2,1,3,12,13,14,15,4,5,16,17,6,7,18,19,8,9,23,24,25,26,27,28,29,34,
%T 35,36,37,38,39,45,46,47,48,49,56,57,58,59,67,68,69,78,79,89,120,10,
%U 20,21,30,31,32,40,41,42,43,50,51,52,53,54,60,61,62,63,64,65,70,71,72,73,74,75,76,80,81,82,83,84,85,86,87,90,91
%N Lexicographically first sequence of different terms, starting with a(1) = 0 and showing a 1-step roller coaster of digits (see the Comments section).
%C After the digit 0 that starts the sequence, we have the 2nd digit of the sequence that is > 0, then the 3rd digit that is < the 2nd digit, then the 4th digit that is > the 3rd digit, the 5th digit that is < the 4th digit, etc. Considering the sequence from the digit-size point of view, we could see it as a kind of roller coaster going up one step, than down one step, than up a again one step, etc.
%C 2-step, 3-step,... 8-step, 9-step roller-coasters sequences will be added soon to the database.
%C This is not a derangement of the positive integers (completed with 0) as integers like 11, 100 or 123 will never appear.
%H Jean-Marc Falcoz, <a href="/A317548/b317548.txt">Table of n, a(n) for n = 1..15002</a>
%e The sequence starts with 0,2,1,3,12,13,14,15,4,5,16... and indeed the digits form a kind of 1-step roller-coaster 0 < 2 > 1 < 3 > 1 < 2 > 1 < 3 > 1 < 4 > 1 < 4...
%Y A289263 (Number of maximal roller coasters in all n! permutations of n elements), A317549 (2-step roller coaster), A317550 (3-step).
%K nonn,base,look
%O 1,2
%A _Eric Angelini_ and _Jean-Marc Falcoz_, Jul 31 2018
|
