A317548 -id:A317548 - cp's OEIS frontend

A317549 Lexicographically first sequence of different terms, starting with a(1) = 0 and showing a 2-step roller coaster of digits (see the Comments section).

0, 1, 2, 10, 3, 4, 20, 5, 6, 21, 7, 8, 30, 12, 101, 9, 31, 23, 102, 32, 13, 42, 14, 52, 15, 62, 16, 72, 17, 82, 18, 92, 123, 103, 43, 24, 53, 25, 63, 26, 73, 27, 83, 28, 93, 124, 104, 54, 34, 64, 35, 65, 36, 74, 37, 84, 38, 94, 125, 40, 19, 41, 29, 50, 39, 51, 45, 105, 75, 46, 76, 47, 85, 48, 95, 126, 106, 86, 56, 87, 57, 96, 58, 97

Offset: 1

Eric Angelini and Jean-Marc Falcoz, Aug 02 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 two steps, than down two steps, than up a again two steps, etc.

			The sequence starts with 0,1,2,10,3,4,20,5,6,21,7,8,30,... and indeed the digits form a kind of 2-step roller-coaster 0 < 1 < 2 > 1 > 0 < 3 < 4 > 2 > 0 < 5 < 6 > 2 > 1 < 7 < 8 > 3 > 0...

Jean-Marc Falcoz, Table of n, a(n) for n = 1..5004

A317548 (1-step roller coaster)

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).

Original entry on oeis.org

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

Eric Angelini and Jean-Marc Falcoz, Aug 03 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, 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.

			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...

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

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

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).

Original entry on oeis.org

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

Eric Angelini and Jean-Marc Falcoz, Aug 02 2018

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.

			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.

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

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

cp's OEIS Frontend

A317549 Lexicographically first sequence of different terms, starting with a(1) = 0 and showing a 2-step roller coaster of digits (see the Comments section).

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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).

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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).

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