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A293225 Compound filter: a(n) = P(A293224(n), A293223(n)), where P(n,k) is sequence A000027 used as a pairing function.

%I A293225 #9 Oct 18 2017 00:56:12
%S A293225 1,2,2,5,2,8,2,12,4,13,2,32,2,40,30,33,2,59,2,58,42,69,2,143,8,80,29,
%T A293225 83,2,178,2,197,38,96,25,239,2,100,121,163,2,221,2,202,194,103,2,448,
%U A293225 61,365,59,245,2,333,48,576,187,256,2,720,2,278,546,718,138,606,2,503,114,1009,2,1101,2,437,651,678,532,831,2,1400,172,213,2,1508,71,500,597
%N A293225 Compound filter: a(n) = P(A293224(n), A293223(n)), where P(n,k) is sequence A000027 used as a pairing function.
%H A293225 Antti Karttunen, <a href="/A293225/b293225.txt">Table of n, a(n) for n = 1..19683</a>
%F A293225 a(n) = (1/2)*(2 + ((A293224(n) + A293223(n))^2) - A293224(n) - 3*A293223(n)).
%o A293225 (PARI)
%o A293225 rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
%o A293225 A019565(n) = {my(j,v); factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ This function from _M. F. Hasler_
%o A293225 A289813(n) = { my (d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==1, 1, 0)), 2); };
%o A293225 A289814(n) = { my (d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==2, 1, 0)), 2); };
%o A293225 A293221(n) = { my(m=1); fordiv(n,d,if(d < n,m *= A019565(A289813(d)))); m; };
%o A293225 A293222(n) = { my(m=1); fordiv(n,d,if(d < n,m *= A019565(A289814(d)))); m; };
%o A293225 v293223 = rgs_transform(vector(19683,n,A293221(n)));
%o A293225 A293223(n) = v293223[n];
%o A293225 v293224 = rgs_transform(vector(19683,n,A293222(n)));
%o A293225 A293224(n) = v293224[n];
%o A293225 A293225(n) = (1/2)*(2 + ((A293224(n) + A293223(n))^2) - A293224(n) - 3*A293223(n));
%o A293225 (Scheme) (define (A293225 n) (* 1/2 (+ (expt (+ (A293224 n) (A293223 n)) 2) (- (A293224 n)) (- (* 3 (A293223 n))) 2)))
%Y A293225 Cf. A000027, A019565, A293221, A293222, A293223, A293224, A293226 (rgs-version of this filter).
%Y A293225 Cf. also A289813, A289814, A290093, A290094.
%K A293225 nonn
%O A293225 1,2
%A A293225 _Antti Karttunen_, Oct 03 2017