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A143206 Product of the n-th cousin prime pair. 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

intersection of A143203 and A001358.

Solutions of the equation n'=2*sqrt(n+4), where n' is the arithmetic derivative of n. [Paolo P. Lava, Oct 30 2012]

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

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Cousin Primes

EXAMPLE

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.

MAPLE

with(numtheory);

A143206:= proc(i)

local n, p;

for n from 1 to i do

  if n*add(op(2, p)/op(1, p), p=ifactors(n)[2])=2*sqrt(n+4) then print(n); fi;

od; end:

A143206(1000000);  # Paolo P. Lava, Oct 30 2012

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 *)

PROG

(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

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

CROSSREFS

Cf. A037074, A111192.

Sequence in context: A218960 A218955 A085027 * A182754 A045559 A144314

Adjacent sequences:  A143203 A143204 A143205 * A143207 A143208 A143209

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Aug 12 2008

STATUS

approved

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Last modified November 15 09:03 EST 2019. Contains 329144 sequences. (Running on oeis4.)