%I
%S 1,3,5,9,5,19,5,26,18,19,5,51,5,19,40,73,5,72,5,72,40,40,5,113,31,19,
%T 83,111,8,129,5,101,32,19,32,221,8,19,40,179,8,199,5,84,159,40,8,312,
%U 13,84,82,84,8,239,49,261,32,82,23,419,5,19,159,224,82,334,8,84,32,334,8,543,8,32,84,84,82,285,5,243,332,32,57,478,40,32,32,218,23,419,82
%N Compound filter (prime signature of n & prime signature of the nth Jacobsthal number): a(n) = P(A101296(n), A286566(n)), where P(n,k) is sequence A000027 used as a pairing function.
%C Here, instead of A046523 and A278165 we use as the components of a(n) their rgsversions A101296 and A286565 because of the latter sequences' more moderate growth rates.
%H Antti Karttunen, <a href="/A286566/b286566.txt">Table of n, a(n) for n = 1..1032</a> (computed using the bfile of A278165 provided by Hans Havermann)
%F a(n) = (1/2)*(2 + ((A101296(n)+A286565(n))^2)  A101296(n)  3*A286565(n)).
%o (Scheme) (define (A286566 n) (* (/ 1 2) (+ (expt (+ (A101296 n) (A286565 n)) 2) ( (A101296 n)) ( (* 3 (A286565 n))) 2)))
%Y Cf. A001045, A046523, A101296, A278165, A286565.
%Y Cf. A000978 (positions of 5's).
%Y Cf. A286467 (similar filter).
%K nonn
%O 1,2
%A _Antti Karttunen_, May 21 2017
