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

1,2

Comments

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.

Links

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

Example

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...

Crossrefs

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

Sequence in context: A175243 A168217 A329025 * A320327 A366591 A007447

Adjacent sequences: A317545 A317546 A317547 * A317549 A317550 A317551

Keyword

nonn,base,look

Author

Eric Angelini and Jean-Marc Falcoz, Jul 31 2018

Status

approved