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%I #9 Jul 26 2017 09:28:45
%S 1,3,2,3,10,5,2,5,7,3,21,5,10,36,14,5,27,12,2,5,16,5,14,23,7,12,29,3,
%T 21,5,21,78,27,5,27,12,10,78,14,36,136,44,14,90,25,5,27,23,27,90,61,
%U 12,42,38,2,5,16,5,14,23,16,23,67,5,27,23,14,44,40,23,61,80,7,12,67,12,25,80,29,38,121,3,21,5,21,78,27,5,27,12,21,465,27,78,300,90,27
%N Compound filter (for base-3 digit runlengths): a(n) = P(A290091(n), A290092(n)), where P(n,k) is sequence A000027 used as a pairing function.
%C For all i, j: a(i) = a(j) => A006047(i) = A006047(j) => A053735(i) = A053735(j).
%H Antti Karttunen, <a href="/A290093/b290093.txt">Table of n, a(n) for n = 0..19683</a>
%F a(n) = (1/2)*(2 + ((A290091(n)+A290092(n))^2) - A290091(n) - 3*A290092(n)).
%o (Scheme) (define (A290093 n) (* (/ 1 2) (+ (expt (+ (A290091 n) (A290092 n)) 2) (- (A290091 n)) (- (* 3 (A290092 n))) 2)))
%Y Cf. A000027, A278222, A289813, A289814, A290091, A290092.
%Y Cf. A006047, A053735, A290079 (some of the matched sequences).
%K nonn
%O 0,2
%A _Antti Karttunen_, Jul 25 2017
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