A226222 a(1) = a(2) = a(3) = 1, a(n) = a(n-2-a(n-2)) + a(n-1-a(n-3)) for n>3.

1, 1, 1, 2, 2, 3, 3, 3, 4, 5, 5, 5, 6, 6, 7, 7, 8, 9, 9, 9, 10, 10, 11, 11, 11, 12, 13, 13, 13, 14, 15, 16, 16, 16, 17, 18, 18, 18, 18, 19, 20, 21, 21, 21, 21, 22, 22, 23, 23, 24, 25, 25, 25, 26, 26, 27, 27, 28, 29, 30, 30, 30, 31, 32, 32, 32, 32, 33, 35, 35

Offset: 1

Author

Reinhard Zumkeller, May 31 2013

Keywords

• nonn
• look

Comments

First numbers not occurring: 62, 66, 75, 79, 114, 123, ... .

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Hofstadter's Q-Sequence
• Wikipedia, Hofstadter sequence
• Index entries for Hofstadter-type sequences

Crossrefs

Cf. A005185, A046699, A063892, A070867.

Programs

Haskell

a226222 n = a226222_list !! (n-1)
a226222_list = 1 : 1 : 1 : zipWith (+)
   (map a226222 $ zipWith (-) [3..] a226222_list)
   (map a226222 $ zipWith (-) [2..] $ tail a226222_list)
-- Reinhard Zumkeller, May 31 2013

Mathematica

a[n_]:= a[n]= If[n<4, 1, a[n-2 -a[n-2]] + a[n-1 -a[n-3]]];
Table[a[n], {n, 80}] (* G. C. Greubel, Mar 28 2022 *)

Sage

@CachedFunction
def a(n): # A226222
    if (n<4): return 1
    else: return  a(n-2-a(n-2)) + a(n-1-a(n-3))
[a(n) for n in (1..80)] # G. C. Greubel, Mar 28 2022

Formula

a(n) = a(n-2 - a(n-2)) + a(n-1 - a(n-3)), with a(1) = a(2) = a(3) = 1.