A289263 -id:A289263 - cp's OEIS frontend

A317548 Lexicographically first sequence of different terms, starting with a(1) = 0 and showing a 1-step roller coaster of digits (see the Comments section).

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, 35, 36, 37, 38, 39, 45, 46, 47, 48, 49, 56, 57, 58, 59, 67, 68, 69, 78, 79, 89, 120, 10, 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

Offset: 1

Eric Angelini and Jean-Marc Falcoz, Jul 31 2018

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.
2-step, 3-step,... 8-step, 9-step roller-coasters sequences will be added soon to the database.
This is not a derangement of the positive integers (completed with 0) as integers like 11, 100 or 123 will never appear.

			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...

Jean-Marc Falcoz, Table of n, a(n) for n = 1..15002

A289263 (Number of maximal roller coasters in all n! permutations of n elements), A317549 (2-step roller coaster), A317550 (3-step).

cp's OEIS Frontend

A317548 Lexicographically first sequence of different terms, starting with a(1) = 0 and showing a 1-step roller coaster of digits (see the Comments section).

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