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

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

10,4

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.

It would make sense to define a(n) = 0 for n = 0, ..., 9.

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)

Links

T. D. Noe, Table of n, a(n) for n = 10..10000

E. Angelini, The Ghost Iteration, Personal blog "Cinquante signes", Nov 2019

Formula

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

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

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

Sequence in context: A064834 A040163 A113608 * A080465 A347689 A151950

Adjacent sequences: A040112 A040113 A040114 * A040116 A040117 A040118

Keyword

nonn,base,easy

Author

Felice Russo

Extensions

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

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

Status

approved