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%I #6 Oct 02 2017 18:59:00
%S 1,5,10,13,21,65,78,25,36,189,21,89,210,189,406,41,55,90,666,103,210,
%T 119,78,348,231,44,1378,251,171,1769,1830,61,78,2277,253,701,45,230,
%U 465,900,1485,3485,36,463,66,90,55,816,1176,495,5050,1429,78,5777,666,777,406,1034,78,349,6105,230,5050,85,105,8645,171,739,2346,9729,1081
%N Compound filter (multiplicative order of 2 mod 2n+1 & number of trailing 1's in binary expansion of 2n+1): a(n) = P(A002326(n), A007814(2n+2)), where P(n,k) is sequence A000027 used as a pairing function.
%H Antti Karttunen, <a href="/A292268/b292268.txt">Table of n, a(n) for n = 0..10000</a>
%F a(n) = (1/2)*(2 + ((A002326(n) + A007814(2n+2))^2) - A002326(n) - 3*A007814(2n+2)).
%o (PARI)
%o A002326(n) = if(n<0, 0, znorder(Mod(2, 2*n+1))); \\ This function from _Michael Somos_, Mar 31 2005
%o A007814(n) = valuation(n,2);
%o A292268(n) = (1/2)*(2 + ((A002326(n)+A007814(2*(1+n)))^2) - A002326(n) - 3*A007814(2*(1+n)));
%o (Scheme) (define (A292268 n) (* 1/2 (+ (expt (+ (A002326 n) (A007814 (+ 2 n n))) 2) (- (A002326 n)) (- (* 3 (A007814 (+ 2 n n)))) 2)))
%Y Cf. A000027, A002326, A007814, A292267 (rgs-version of this filter).
%Y Cf. also A291755, A292249.
%K nonn
%O 0,2
%A _Antti Karttunen_, Oct 02 2017
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