A240808 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.

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

Offset: 0

Author

N. J. A. Sloane, Apr 15 2014

Keywords

• nonn
• look

Comments

a(A241218(n)) = n and a(m) <> n for m < A241218(n). - Reinhard Zumkeller, Apr 17 2014

References

• 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]

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..20000
• Rémy Sigrist, Colored scatterplot of a(n) for n = 0..20000 (where the color is function of n mod 3)
• Index entries for Hofstadter-type sequences

Crossrefs

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

Trisections: A244780..A244782.

Programs

Haskell

a240808 n = a240808_list !! n
a240808_list = 2 : 1 : 0 : zipWith (+) xs (tail xs)
   where xs = map a240808 $ zipWith (-) [1..] $ tail a240808_list
-- Reinhard Zumkeller, Apr 17 2014

Maple

a:=proc(n) option remember; global k;
if n = 0 then 2
elif n = 1 then 1
elif n = 2 then 0
else
if (a(n-1) <= n-1) and (a(n-2) <= n-2) then
a(n-1-a(n-1))+a(n-2-a(n-2));
else lprint("died with n =",n); return (-1);
fi;
fi; end;
[seq(a(n),n=0..100)];

Mathematica

a[n_] := a[n] = Switch[n, 0, 2, 1, 1, 2, 0, _,
   If[a[n - 1] <= n - 1 && a[n - 2] <= n - 2,
   a[n - 1 - a[n - 1]] + a[n - 2 - a[n - 2]],
   Print["died with n =", n]; Return[-1]]];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Oct 02 2024 *)