A239913 a(n) = n - Q(n), where Q(n) is Hofstadter's Q-sequence A005185.

0, 1, 1, 1, 2, 2, 2, 3, 3, 4, 5, 4, 5, 6, 5, 7, 7, 7, 8, 8, 9, 10, 11, 8, 11, 12, 11, 12, 13, 14, 11, 15, 16, 14, 14, 17, 17, 16, 18, 18, 18, 19, 19, 20, 21, 22, 23, 16, 25, 25, 21, 24, 27, 24, 25, 28, 25, 28, 27, 28, 29, 30, 23, 31, 34, 28, 32, 35, 30, 30, 34, 34, 33, 35

Offset: 1

Author

N. J. A. Sloane, Apr 09 2014

Keywords

• nonn

Comments

Just as for A005185, it is not known if this sequence exists for all n.

Crossrefs

Cf. A005185.

Programs

Python

from functools import lru_cache
@lru_cache(maxsize=None)
def A239913(n): return n-1 if n<=2 else A239913(a:=1+A239913(n-1))+A239913(b:=2+A239913(n-2))-a-b+n # Chai Wah Wu, Apr 13 2023

Formula

For n >= 3, a(n) = a(a(n-1)+1) + a(a(n-2)+2) - a(n-1) - a(n-2) + n - 3. - Chai Wah Wu, Apr 13 2023