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A040115
Concatenate absolute values of differences between adjacent digits of n.
32
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
0,14
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)
LINKS
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. A329200, A329201: iterations of n +- a(n).
Sequence in context: A064834 A040163 A113608 * A080465 A347689 A151950
KEYWORD
nonn,base,easy
AUTHOR
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
STATUS
approved