A317550 Lexicographically first sequence of different terms, starting with a(1) = 0 and showing a 3-step roller coaster of digits (see the Comments section).

0, 1, 2, 3, 210, 4, 5, 6, 32, 12, 7, 8, 42, 13, 45, 43, 14, 56, 52, 15, 67, 53, 16, 78, 54, 17, 89, 62, 123, 9, 63, 23, 46, 310, 18, 92, 10, 24, 64, 20, 25, 65, 21, 26, 72, 101, 27, 320, 28, 93, 102, 34, 321, 35, 73, 103, 47, 410, 36, 74, 30, 37, 82, 104, 57, 420, 38, 94, 31, 48, 95, 40, 58, 96, 41

Offset: 1

Author

Eric Angelini and Jean-Marc Falcoz, Aug 03 2018

Keywords

• base
• nonn
• look

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, then the 5th digit that is < the 4th digit, then the 6th digit that is < the 5th digit, etc. Considering the sequence from the digit-size point of view, we could see it as a kind of roller coaster going up three steps, than down three steps, than up a again three steps, etc.

Examples

			The sequence starts with 0,1,2,3,210,4,5,6,32,12,7,8,42,13,... and indeed the digits form a kind of 3-step roller-coaster 0 < 1 < 2 < 3 > 2 > 1 > 0 < 4 < 5 < 6 > 3 > 2 > 1 < 2 < 7 < 8 > 4 > 2 > 1...
		

Links

• Jean-Marc Falcoz, Table of n, a(n) for n = 1..2005

Crossrefs

Cf. A317548 (1-step roller coaster) and A317549 (2-step roller coaster).