A240808 - OEIS

%I #25 Oct 02 2024 06:47:46

%S 2,1,0,2,1,3,2,1,3,5,4,3,5,4,6,8,4,6,8,7,9,8,7,12,11,7,12,14,10,12,14,

%T 10,12,17,13,12,20,16,12,20,19,15,20,19,18,23,19,21,26,19,21,26,19,24,

%U 29,19,27,32,19,27,32,22,30,32,22,30,32,25,33,32,28,36,32,31,39,32,31,42,35,31,45,38,31,45,38,31,48,41,31,51,44,31,51,47,34

%N a(0)=2, a(1)=1, a(2)=0; thereafter a(n) = a(n-1-a(n-1))+a(n-2-a(n-2)) unless a(n-1) <= n-1 or a(n-2) <= n-2 in which case the sequence terminates.

%C a(A241218(n)) = n and a(m) <> n for m < A241218(n). - _Reinhard Zumkeller_, Apr 17 2014

%D Higham, Jeff and Tanny, Stephen, A tamely chaotic meta-Fibonacci sequence. Twenty-third Manitoba Conference on Numerical Mathematics and Computing (Winnipeg, MB, 1993). Congr. Numer. 99 (1994), 67-94. [Contains a detailed analysis of this sequence]

%H Reinhard Zumkeller, <a href="/A240808/b240808.txt">Table of n, a(n) for n = 0..20000</a>

%H Rémy Sigrist, <a href="/A240808/a240808.png">Colored scatterplot of a(n) for n = 0..20000</a> (where the color is function of n mod 3)

%H <a href="/index/Ho#Hofstadter">Index entries for Hofstadter-type sequences</a>

%p a:=proc(n) option remember; global k;

%p if n = 0 then 2

%p elif n = 1 then 1

%p elif n = 2 then 0

%p else

%p if (a(n-1) <= n-1) and (a(n-2) <= n-2) then

%p a(n-1-a(n-1))+a(n-2-a(n-2));

%p else lprint("died with n =",n); return (-1);

%p fi;

%p fi; end;

%p [seq(a(n),n=0..100)];

%t a[n_] := a[n] = Switch[n, 0, 2, 1, 1, 2, 0, _,

%t    If[a[n - 1] <= n - 1 && a[n - 2] <= n - 2,

%t    a[n - 1 - a[n - 1]] + a[n - 2 - a[n - 2]],

%t    Print["died with n =", n]; Return[-1]]];

%t Table[a[n], {n, 0, 100}] (* _Jean-François Alcover_, Oct 02 2024 *)

%o (Haskell)

%o a240808 n = a240808_list !! n

%o a240808_list = 2 : 1 : 0 : zipWith (+) xs (tail xs)

%o    where xs = map a240808 $ zipWith (-) [1..] $ tail a240808_list

%o -- _Reinhard Zumkeller_, Apr 17 2014

%Y A006949 and A240807 have the same recurrence but different initial conditions.

%Y Trisections: A244780..A244782.

%K nonn,look

%O 0,1

%A _N. J. A. Sloane_, Apr 15 2014