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A176982 Sequence defined by the recursion a(n) = (1/2)*((1-signum(abs(b(n))-n))*b(n)+(1+signum(abs(b(n))-n))*a(n-1)), with a(1)=1 and b(n)=1+a(n-1-(n mod a(n-1)))-(-1)^n*a(n-1). 1


%S 1,1,2,1,3,1,3,1,3,-1,-1,1,3,-3,-5,3,1,1,3,-1,-1,1,3,1,3,1,3,-1,-1,1,

%T 3,-3,-5,5,11,-13,-9,21,21,-21,-21,1,3,-23,-21,1,3,1,3,1,3,-1,-1,1,3,

%U -3,-5,7,11,-9,-9,9,19,-21,-11,1,3,-13,-33,23,11,-21,-11,1,3,-1,-1,1,3,-3

%N Sequence defined by the recursion a(n) = (1/2)*((1-signum(abs(b(n))-n))*b(n)+(1+signum(abs(b(n))-n))*a(n-1)), with a(1)=1 and b(n)=1+a(n-1-(n mod a(n-1)))-(-1)^n*a(n-1).

%C Behaves erratically (see linked picture).

%C There is a similar sequence with a(1)=2.

%D G. Balzarotti and P. P. Lava, 103 curiosità matematiche, Hoepli, 2010, p. 276.

%H Paolo P. Lava, <a href="/A176982/b176982.txt">Table of n, a(n) for n = 1..10000</a>

%H Paolo P. Lava, <a href="/a176982.pdf">Graph of the first 600 terms of the sequence</a>

%H John A. Pelesko, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL7/Pelesko/pel11.html">Generalizing the Conway-Hofstadter $10,000 Sequence</a>, Journal of Integer Sequences, Vol. 7 (2004), Article 04.3.5.

%H Klaus Pinn, <a href="http://arxiv.org/abs/cond-mat/9808031">A Chaotic Cousin Of Conway's Recursive Sequence</a>, arXiv:cond-mat/9808031, 1998.

%F a(n) = (1/2)*((1-signum(abs(b(n))-n))*b(n)+(1+signum(abs(b(n))-n))*a(n-1)), with a(1)=1 and b(n)=1+a(n-1-(n mod a(n-1)))-(-1)^n*a(n-1).

%e a(1)=1.

%e b(2)=signum(abs(1+(2-1-(2 mod 1))-(-1)^2*1)-2)=signum(abs(1+1-1)-2)=-1.

%e a(2)=(1/2)*(1+1)*1+(1/2)*(1-1)*1=1+0=1.

%p P:=proc(i) local a,n; a:=array(1..50000); a[1]:=1; print(a[1]); for n from 2 by 1 to i do a[n]:=1/2*(1-signum(abs(1+a[n-1-(n mod (a[n-1]))]-(-1)^n*a[n-1])-n))*(1+a[n-1-(n mod (a[n-1]))]-(-1)^n*a[n-1])+1/2*(1+signum(abs(1+a[n-1-(n mod (a[n-1]))]-(-1)^n*a[n-1])-n))*a[n-1]; print(a[n]); od; end: P(10000);

%Y Cf. A004001, A176075, A176076.

%K sign,look

%O 1,3

%A _Paolo P. Lava_ and _Giorgio Balzarotti_, Apr 30 2010

%E Entries and formula corrected by _Paolo P. Lava_, May 04 2010

%E a(3) corrected by _N. J. A. Sloane_, Oct 02 2010

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Last modified May 18 23:41 EDT 2021. Contains 344009 sequences. (Running on oeis4.)