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A040115 Concatenate absolute values of differences between adjacent digits of n. 26


%S 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,

%T 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,

%U 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 Concatenate absolute values of differences between adjacent digits of n.

%C 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 From _M. F. Hasler_, Nov 09 2019: (Start)

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

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

%C 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 T. D. Noe, <a href="/A040115/b040115.txt">Table of n, a(n) for n = 10..10000</a>

%H E. Angelini, <a href="http://cinquantesignes.blogspot.com/2019/11/the-ghost-iteration.html">The Ghost Iteration</a>, Personal blog "Cinquante signes", Nov 2019

%e a(371) = 46, for example.

%e a(110) = 01 = 1, while A080465(110) = 10 - 1 = 9. - _M. F. Hasler_, Nov 09 2019

%o (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 Cf. A037904, A040114, A040163, A040997.

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

%K nonn,base,easy

%O 10,4

%A _Felice Russo_

%E Definition clarified by _N. J. A. Sloane_, Aug 19 2008

%E Name edited by _M. F. Hasler_, Nov 09 2019

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Last modified April 9 10:32 EDT 2020. Contains 333348 sequences. (Running on oeis4.)