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

0,1

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

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 *)

Prog

(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

Crossrefs

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

Trisections: A244780..A244782.

Sequence in context: A153247 A071432 A194508 * A263142 A025253 A356261

Adjacent sequences: A240805 A240806 A240807 * A240809 A240810 A240811

Keyword

nonn,look

Author

N. J. A. Sloane, Apr 15 2014

Status

approved