A335493 The successive absolute differences between two digits are the successive differences between two terms. See in the Comments section why a(n) = a(n-1) sometimes.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 17, 23, 28, 29, 30, 36, 42, 49, 55, 58, 61, 64, 66, 68, 70, 75, 79, 79, 79, 82, 84, 89, 94, 96, 98, 98, 98, 100, 101, 108, 115, 117, 119, 121, 123, 125, 127, 129, 130, 136, 142, 146, 150, 151, 151, 156, 161, 164, 167, 168, 169, 170, 171, 172, 179, 180, 180, 181, 182, 183, 183

Offset

1,3

Comments

To extend the sequence S with a new term a(n), we always add to a(n-1) the last absolute difference D between two digits that must be considered. As a term of S can have two successive identical digits [like a(19) = 55 here], or, in general, as two successive digits of S can be identical, we will see sometimes in S two or more equal terms following each other [like a(27) = a(28) = a(29) = 73 here].

Links

Carole Dubois, Table of n, a(n) for n = 1..5002

Example

After a(10) = 9, we cannot extend S with a(11) < 17 as the difference between a(10) and a(11) cannot be < 8, this 8 being the difference between 9 and the first digit of a(11);
After a(11) = 17, we are driven by the next absolute difference between digits, which is 6 (the difference between the 1 and the 7 of 17). We add this 6 to a(11) = 17 to get a(12) = 23; etc.
We have seen in the Comments section why we sometimes have to add 0 to a(n), which leads to a(n+1) = a(n).

Crossrefs

Cf. A335492 [same idea but a(n) is sometimes < a(n-1)].

Sequence in context: A304247 A304245 A304244 * A319725 A048408 A199343

Adjacent sequences: A335490 A335491 A335492 * A335494 A335495 A335496

Keyword

base,nonn

Author

Eric Angelini and Carole Dubois, Jun 11 2020

Status

approved