A143206 Product of the n-th cousin prime pair.

21, 77, 221, 437, 1517, 2021, 4757, 6557, 9797, 11021, 12317, 16637, 27221, 38021, 50621, 53357, 77837, 95477, 99221, 123197, 145157, 159197, 194477, 210677, 216221, 239117, 250997, 378221, 416021, 455621, 549077, 576077, 594437, 680621

Offset: 1

Author

Reinhard Zumkeller, Aug 12 2008

Keywords

• nonn

Comments

Intersection of A143203 and A001358.

Sum_{n>=2} 1/a(n) > 0.02187310784. - R. J. Mathar, Jan 23 2013

Examples

			a(1) = 3*7 = 3*(3+4) = 21;
a(2) = 7*11 = 7*(7+4) = 77;
a(3) = 13*17 = 13*(13+4) = 221;
a(4) = 19*23 = 19*(19+4) = 437.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Cousin Primes

Crossrefs

Cf. A037074, A111192.

Programs

Haskell

a143206 n = a143206_list !! (n-1)
a143206_list = (3*7) : f a000040_list where
   f (p:ps@(p':_)) | p'-p == 4 = (p*p') : f ps
                   | otherwise = f ps
-- Reinhard Zumkeller, Sep 13 2011

Magma

[(p*(p+4)): p in PrimesUpTo(1000)| IsPrime(p+4)]; // Vincenzo Librandi, Jan 04 2018

Mathematica

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 *)

PARI

lista(nn) = forprime(p=2, nn, if (isprime(q=p+4), print1(p*q, ", "))); \\ Michel Marcus, Jan 04 2018

Formula

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