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Compound filter (the left & right summand of Hofstadter-Conway $10000 sequence): a(n) = P(A004001(A004001(n-1)), A004001(n-A004001(n-1))), where P(n,k) is sequence A000027 used as a pairing function, with a(1) = a(2) = 0.
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%I #8 May 18 2017 21:48:30

%S 0,0,1,1,2,5,5,5,8,13,19,19,25,25,25,25,32,41,51,62,62,73,86,86,99,99,

%T 99,113,113,113,113,113,128,145,163,182,202,202,222,244,267,267,290,

%U 315,315,340,340,340,366,394,394,422,422,422,451,451,451,451,481,481,481,481,481,481,512,545,579,614,650,687,687,724,763,803,844,844,885,928,972,972

%N Compound filter (the left & right summand of Hofstadter-Conway $10000 sequence): a(n) = P(A004001(A004001(n-1)), A004001(n-A004001(n-1))), where P(n,k) is sequence A000027 used as a pairing function, with a(1) = a(2) = 0.

%H Antti Karttunen, <a href="/A286541/b286541.txt">Table of n, a(n) for n = 1..16384</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PairingFunction.html">Pairing Function</a>

%F a(1) = a(2) = 0, for n > 2, a(n) = (1/2)*(2 + ((A004001(A004001(n-1))+A004001(n-A004001(n-1)))^2) - A004001(A004001(n-1)) - 3*A004001(n-A004001(n-1))).

%o (Scheme) (define (A286541 n) (if (<= n 2) 0 (* (/ 1 2) (+ (expt (+ (A004001 (A004001 (- n 1))) (A004001 (- n (A004001 (- n 1))))) 2) (- (A004001 (A004001 (- n 1)))) (- (* 3 (A004001 (- n (A004001 (- n 1)))))) 2))))

%Y Cf. A004001, A286559, A286560.

%Y Cf. A283468, A283469, A283470, A283472 and also A283471, A283473.

%K nonn

%O 1,5

%A _Antti Karttunen_, May 18 2017