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

%I A040115 #42 Dec 21 2024 11:56:03
%S A040115 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,
%T A040115 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,
%U A040115 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
%N A040115 Concatenate absolute values of differences between adjacent digits of n.
%C A040115 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.
%C A040115 From _M. F. Hasler_, Nov 09 2019: (Start)
%C A040115 This sequence coincides with A080465 up to a(109) but is thereafter completely different.
%C A040115 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)
%H A040115 T. D. Noe, <a href="/A040115/b040115.txt">Table of n, a(n) for n = 0..10000</a>
%H A040115 E. Angelini, <a href="http://cinquantesignes.blogspot.com/2019/11/the-ghost-iteration.html">The Ghost Iteration</a>, Personal blog "Cinquante signes", Nov 2019
%H A040115 E. Angelini, <a href="/A040115/a040115.pdf">The Ghost Iteration</a>, Personal blog "Cinquante signes", Nov 2019 [Cached copy, pdf file, with permission]
%F A040115 a(n) = 0 iff n is a repdigit >= 11 (A010785). - _Bernard Schott_, May 09 2022
%e A040115 a(371) = 46, for example.
%e A040115 a(110) = 01 = 1, while A080465(110) = 10 - 1 = 9. - _M. F. Hasler_, Nov 09 2019
%t A040115 Table[FromDigits[Abs[Differences[IntegerDigits[n]]]],{n,110}] (* _Harvey P. Dale_, Dec 16 2021 *)
%o A040115 (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
%Y A040115 Cf. A010785, A037904, A040114, A040163, A040997.
%Y A040115 Cf. A329200, A329201: iterations of n +- a(n).
%K A040115 nonn,base,easy
%O A040115 0,14
%A A040115 _Felice Russo_
%E A040115 Definition clarified by _N. J. A. Sloane_, Aug 19 2008
%E A040115 Name edited by _M. F. Hasler_, Nov 09 2019
%E A040115 Terms a(0) = a(1) = ... = a(9) = 0 prepended by _Max Alekseyev_, Jul 26 2024