This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A286541 #9 Feb 16 2025 08:33:45 %S A286541 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 A286541 99,113,113,113,113,113,128,145,163,182,202,202,222,244,267,267,290, %U A286541 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 A286541 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 A286541 Antti Karttunen, <a href="/A286541/b286541.txt">Table of n, a(n) for n = 1..16384</a> %H A286541 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PairingFunction.html">Pairing Function</a> %F A286541 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 A286541 (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 A286541 Cf. A004001, A286559, A286560. %Y A286541 Cf. A283468, A283469, A283470, A283472 and also A283471, A283473. %K A286541 nonn %O A286541 1,5 %A A286541 _Antti Karttunen_, May 18 2017