A040115 Concatenate absolute values of differences between adjacent digits of n.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1

Offset: 0

Author

Felice Russo

Keywords

• nonn
• base
• easy

Comments

Let the decimal expansion of n be abcd...efg, say. Then a(n) has decimal expansion |a-b| |b-c| |c-d| ... |e-f| |f-g|. Leading zeros in a(n) are omitted.

From M. F. Hasler, Nov 09 2019: (Start)

This sequence coincides with A080465 up to a(109) but is thereafter completely different.

Eric Angelini calls a(n) the "ghost" of the number n and considers iterations of n -> n +- a(n) depending on parity of a(n), cf. A329200 and A329201. (End)

Examples

			a(371) = 46, for example.
a(110) = 01 = 1, while A080465(110) = 10 - 1 = 9. - _M. F. Hasler_, Nov 09 2019
		

Links

• T. D. Noe, Table of n, a(n) for n = 0..10000
• E. Angelini, The Ghost Iteration, Personal blog "Cinquante signes", Nov 2019
• E. Angelini, The Ghost Iteration, Personal blog "Cinquante signes", Nov 2019 [Cached copy, pdf file, with permission]

Crossrefs

Cf. A010785, A037904, A040114, A040163, A040997.

Cf. A329200, A329201: iterations of n +- a(n).

Programs

Mathematica

Table[FromDigits[Abs[Differences[IntegerDigits[n]]]],{n,110}] (* Harvey P. Dale, Dec 16 2021 *)

PARI

apply( A040115(n)=fromdigits(abs((n=digits(n+!n))[^-1]-n[^1])), [10..199]) \\ Works for all n >= 0. - M. F. Hasler, Nov 09 2019

Formula

a(n) = 0 iff n is a repdigit >= 11 (A010785). - Bernard Schott, May 09 2022

Extensions

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

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

Terms a(0) = a(1) = ... = a(9) = 0 prepended by Max Alekseyev, Jul 26 2024