A362257 a(n) = 2*Q(n) - n, where Q(n) is Hofstadter's Q-sequence A005185.

1, 0, 1, 2, 1, 2, 3, 2, 3, 2, 1, 4, 3, 2, 5, 2, 3, 4, 3, 4, 3, 2, 1, 8, 3, 2, 5, 4, 3, 2, 9, 2, 1, 6, 7, 2, 3, 6, 3, 4, 5, 4, 5, 4, 3, 2, 1, 16, -1, 0, 9, 4, -1, 6, 5, 0, 7, 2, 5, 4, 3, 2, 17, 2, -3, 10, 3, -2, 9, 10, 3, 4, 7, 4, 5, 2, 7, 2, 3, 6, 7, 4, 3, 8

Offset: 1

Author

Nathan Fox and Alexis Ducote, Apr 13 2023

Keywords

• sign

Comments

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

A005185 and this sequence exist as long |a(n)| remains less than n.

Crossrefs

Cf. A005185, A239913.

Programs

Python

from functools import lru_cache
@lru_cache(maxsize=None)
def A362257(n): return 2-n if n <= 2 else ((a:=1-A362257(n-1))+(b:=2-A362257(n-2))>>1)+A362257(n+a>>1)+A362257(n+b>>1) # Chai Wah Wu, Apr 13 2023

Formula

a(1) = 1, a(2) = 0; a(n) = (1/2)*(3 - a(n-1) - a(n-2)) + a((1/2)*(n + 1 - a(n-1))) + a((1/2)*(n + 2 - a(n-2))) for n >= 3.