A317630 Lexicographically first sequence of different terms, starting with a(1) = 0 and showing a 1-step roller coaster of terms together with a 1-step roller coaster of digits (see the Comments section).

0, 2, 1, 4, 3, 6, 5, 8, 7, 80, 9, 13, 12, 15, 14, 17, 16, 19, 18, 24, 23, 26, 25, 28, 27, 34, 29, 36, 35, 38, 37, 45, 39, 47, 46, 49, 48, 57, 56, 59, 58, 68, 67, 120, 10, 21, 20, 31, 30, 40, 32, 42, 41, 50, 43, 52, 51, 54, 53, 61, 60, 63, 62, 65, 64, 71, 70, 73, 72, 75, 74, 81, 76, 83, 82, 85, 84, 87, 86, 91, 90, 93, 92, 95

Offset: 1

Author

Eric Angelini and Jean-Marc Falcoz, Aug 02 2018

Keywords

• nonn
• base
• look

Comments

Every term a(n) > 0 of the sequence stands between two terms bigger than a(n) or between two terms smaller than a(n); this is also true for every digit d > 0 of the sequence that stands between two digits bigger than d or between two digits smaller than d.

Examples

			The sequence starts with 0,2,1,4,3,6,5,8,7,80,9,13,12,15,14,17,16,19...
If we consider the terms, we see indeed that 0 < 2 > 1 < 4 > 3 < 6 > 5 < 8 > 7 < 80 > 9 < 13 > 12 < 15 > 14 < 17 > 16 < 19... and if we consider the digits, we see also that 0 < 2 > 1 < 4 > 3 < 6 > 5 < 8 > 7 < 8 > 0 < 9 > 1 < 3 > 1 < 2 > 1 < 5 > 1 < 4 > 1 < 7 > 1 < 6 > 1 < 9...
So no matter the elements considered (terms, digits), those elements seem to ride on a 1-step roller-coaster: up, down, up, down, up, etc.
		

Links

• Lars Blomberg, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A014681 (a 1-step roller coaster of terms only) and A317548 (a 1-step roller coaster of digits only).