login
Product of the n-th cousin prime pair.
8

%I #58 Jul 13 2024 10:13:13

%S 21,77,221,437,1517,2021,4757,6557,9797,11021,12317,16637,27221,38021,

%T 50621,53357,77837,95477,99221,123197,145157,159197,194477,210677,

%U 216221,239117,250997,378221,416021,455621,549077,576077,594437,680621

%N Product of the n-th cousin prime pair.

%C Intersection of A143203 and A001358.

%C Sum_{n>=2} 1/a(n) > 0.02187310784. - _R. J. Mathar_, Jan 23 2013

%H Reinhard Zumkeller, <a href="/A143206/b143206.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CousinPrimes.html">Cousin Primes</a>

%F a(n) = A023200(n)*A046132(n).

%e a(1) = 3*7 = 3*(3+4) = 21;

%e a(2) = 7*11 = 7*(7+4) = 77;

%e a(3) = 13*17 = 13*(13+4) = 221;

%e a(4) = 19*23 = 19*(19+4) = 437.

%t 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 (Haskell)

%o a143206 n = a143206_list !! (n-1)

%o a143206_list = (3*7) : f a000040_list where

%o f (p:ps@(p':_)) | p'-p == 4 = (p*p') : f ps

%o | otherwise = f ps

%o -- _Reinhard Zumkeller_, Sep 13 2011

%o (Magma) [(p*(p+4)): p in PrimesUpTo(1000)| IsPrime(p+4)]; // _Vincenzo Librandi_, Jan 04 2018

%o (PARI) lista(nn) = forprime(p=2, nn, if (isprime(q=p+4), print1(p*q, ", "))); \\ _Michel Marcus_, Jan 04 2018

%Y Cf. A037074, A111192.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Aug 12 2008