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Compound filter (prime signature & prime signature of conjugated prime factorization): a(n) = P(A101296(n), A286621(n)), where P(n,k) is sequence A000027 used as a pairing function.
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%I #10 Feb 16 2025 08:33:45

%S 1,5,8,9,12,32,23,20,13,49,38,51,47,82,49,35,68,51,80,72,124,140,122,

%T 74,18,175,26,111,155,334,192,65,257,280,82,116,255,329,355,99,327,

%U 570,380,177,72,469,437,132,31,72,532,216,498,74,257,144,599,634,597,448,632,745,159,119,784,1044,782,331,907,570,863,186,905,1039,72,384,140,1335,1037

%N Compound filter (prime signature & prime signature of conjugated prime factorization): a(n) = P(A101296(n), A286621(n)), where P(n,k) is sequence A000027 used as a pairing function.

%C Here, instead of A046523 and A278221 we use as the components of a(n) their rgs-versions A101296 and A286621 because of the latter sequence's moderate growth rates.

%C For all i, j: a(i) = a(j) => A286356(i) = A286356(j).

%H Antti Karttunen, <a href="/A286454/b286454.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PairingFunction.html">Pairing Function</a>

%F a(n) = (1/2)*(2 + ((A101296(n)+A286621(n))^2) - A101296(n) - 3*A286621(n)).

%o (Scheme) (define (A286454 n) (* (/ 1 2) (+ (expt (+ (A101296 n) (A286621 n)) 2) (- (A101296 n)) (- (* 3 (A286621 n))) 2)))

%Y Cf. A000027, A046523, A101296, A122111, A278221, A285334, A286621, A286356, A286455, A286456.

%K nonn,changed

%O 1,2

%A _Antti Karttunen_, May 14 2017