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A143206 Product of the n-th cousin prime pair.

%I A143206 #59 Feb 16 2025 08:33:08
%S A143206 21,77,221,437,1517,2021,4757,6557,9797,11021,12317,16637,27221,38021,
%T A143206 50621,53357,77837,95477,99221,123197,145157,159197,194477,210677,
%U A143206 216221,239117,250997,378221,416021,455621,549077,576077,594437,680621
%N A143206 Product of the n-th cousin prime pair.
%C A143206 Intersection of A143203 and A001358.
%C A143206 Sum_{n>=2} 1/a(n) > 0.02187310784. - _R. J. Mathar_, Jan 23 2013
%H A143206 Reinhard Zumkeller, <a href="/A143206/b143206.txt">Table of n, a(n) for n = 1..10000</a>
%H A143206 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CousinPrimes.html">Cousin Primes</a>
%F A143206 a(n) = A023200(n)*A046132(n).
%e A143206 a(1) = 3*7 = 3*(3+4) = 21;
%e A143206 a(2) = 7*11 = 7*(7+4) = 77;
%e A143206 a(3) = 13*17 = 13*(13+4) = 221;
%e A143206 a(4) = 19*23 = 19*(19+4) = 437.
%t A143206 fQ[n_] := Block[{fi = FactorInteger@ n}, Last@# & /@ fi == {1, 1} && Differences[ First@# & /@ fi] == {4}]; Select[ Range@ 700000, fQ] (* _Robert G. Wilson v_, Feb 08 2012 *)
%o A143206 (Haskell)
%o A143206 a143206 n = a143206_list !! (n-1)
%o A143206 a143206_list = (3*7) : f a000040_list where
%o A143206    f (p:ps@(p':_)) | p'-p == 4 = (p*p') : f ps
%o A143206                    | otherwise = f ps
%o A143206 -- _Reinhard Zumkeller_, Sep 13 2011
%o A143206 (Magma) [(p*(p+4)): p in PrimesUpTo(1000)| IsPrime(p+4)]; // _Vincenzo Librandi_, Jan 04 2018
%o A143206 (PARI) lista(nn) = forprime(p=2, nn, if (isprime(q=p+4), print1(p*q, ", "))); \\ _Michel Marcus_, Jan 04 2018
%Y A143206 Cf. A037074, A111192.
%K A143206 nonn
%O A143206 1,1
%A A143206 _Reinhard Zumkeller_, Aug 12 2008