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

1,2

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.

Links

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

Example

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.

Crossrefs

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

Sequence in context: A026262 A026234 A352726 * A282651 A282665 A320283

Adjacent sequences: A317627 A317628 A317629 * A317631 A317632 A317633

Keyword

nonn,base,look

Author

Eric Angelini and Jean-Marc Falcoz, Aug 02 2018

Status

approved