%I #18 Apr 14 2023 02:09:28

%S 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,

%T 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,

%U 10,3,-2,9,10,3,4,7,4,5,2,7,2,3,6,7,4,3,8

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

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

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

%F 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.

%o (Python)

%o from functools import lru_cache

%o @lru_cache(maxsize=None)

%o 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

%Y Cf. A005185, A239913.

%K sign

%O 1,4

%A _Nathan Fox_ and Alexis Ducote, Apr 13 2023