A040114 List of absolute values of differences between digits of 10, 11, 12, ..., listed digit by digit.

1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 0, 1, 1, 1, 2, 1, 3, 1, 4, 1, 5

Offset: 10

Author

Felice Russo

Keywords

• nonn
• base
• less

Comments

Start with the empty sequence. For n = 10, 11, 12, ... do the following. Let the decimal expansion of n be abcd...efg, say. Append the numbers |a-b|, |b-c|, |c-d|, ... |e-f|, |f-g| to the sequence.

The offset is slightly misleading since for n > 99 the index n is in no direct relation with the number whose digits are used to produce a(n), in contrast to A040115 where all digit-differences of n are concatenated, and leading zeros don't appear. For example, a(100) = 1 and a(101) = 0 are the two differences between the digits of 100. Similarly, a(100 + 2k) corresponds to the difference between first and second digit of 100 + k. Therefore, a(120) = 0. - M. F. Hasler, Nov 09 2019

Examples

			From _M. F. Hasler_, Nov 09 2019: (Start)
The first term is the difference between digits of 10, which is 1.
The second term is the difference between digits of 11, which is 0.
The 100th term is the difference between the first two digits of 100, 1-0 = 1.
The 101st term is the difference between the last two digits of 100, 0-0 = 0.
The 120th term is the difference between the first two digits of 110, 1-1 = 0: Here "leading zeros" are preserved, in contrast to A040115 where all digit-wise differences of any n are concatenated to one term, and leading zeros disappear.
(End)
When we reach n = 371, for example, we append 4 and 6 to the sequence.
		

Links

• T. D. Noe, Table of n, a(n) for n = 10..1902

Crossrefs

Cf. A037904, A040115, A040163, A040997.

Programs

Mathematica

Flatten[Table[Abs[Differences[IntegerDigits[n]]],{n,10,200}]] (* Harvey P. Dale, Jun 28 2021 *)

Extensions

Definition clarified by N. J. A. Sloane, Aug 19 2008.

Name edited by M. F. Hasler, Nov 09 2019