cp's OEIS Frontend

A286559 Compound filter (the left & right summand of Hofstadter Q-sequence): a(n) = P(Q(n-Q(n-1)), Q(n-Q(n-2))), where P(n,k) is sequence A000027 used as a pairing function, with a(1) = a(2) = 0.

%I A286559 #9 Feb 16 2025 08:33:45
%S A286559 0,0,1,2,2,5,8,8,13,13,13,25,24,25,41,32,41,50,50,61,61,61,61,113,84,
%T A286559 86,113,113,113,113,181,128,129,181,200,163,182,221,200,221,242,242,
%U A286559 265,265,265,265,265,481,263,290,420,363,314,422,420,365,481,420,481,481,481,481,761,512,452,687,577,513,722,761,650,687,762,723,760,722,842,760,801
%N A286559 Compound filter (the left & right summand of Hofstadter Q-sequence): a(n) = P(Q(n-Q(n-1)), Q(n-Q(n-2))), where P(n,k) is sequence A000027 used as a pairing function, with a(1) = a(2) = 0.
%H A286559 Antti Karttunen, <a href="/A286559/b286559.txt">Table of n, a(n) for n = 1..67390</a>
%H A286559 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PairingFunction.html">Pairing Function</a>
%F A286559 a(1) = a(2) = 0, for n > 2, a(n) = (1/2)*(2 + ((A005185(n-A005185(n-1))+A005185(n-A005185(n-2)))^2) - A005185(n-A005185(n-1)) - 3*A005185(n-A005185(n-2))).
%o A286559 (Scheme) (define (A286559 n) (if (<= n 2) 0 (* (/ 1 2) (+ (expt (+ (A005185 (- n (A005185 (- n 1)))) (A005185 (- n (A005185 (- n 2))))) 2) (- (A005185 (- n (A005185 (- n 1))))) (- (* 3 (A005185 (- n (A005185 (- n 2)))))) 2))))
%Y A286559 Cf. A005185, A283467, A286541, A286560.
%K A286559 nonn
%O A286559 1,4
%A A286559 _Antti Karttunen_, May 18 2017