%I A037074
%S A037074 15,35,143,323,899,1763,3599,5183,10403,11663,19043,22499,32399,36863,
%T A037074 39203,51983,57599,72899,79523,97343,121103,176399,186623,213443,
%U A037074 272483,324899,359999,381923,412163,435599,656099,675683,685583,736163
%N A037074 Products of twin primes.
%C A037074 Except for the first term, all entries have digital root 8. - Lekraj 
               Beedassy (blekraj(AT)yahoo.com), Jun 11 2004
%C A037074 Albert A. Mullin states that m is a product of twin primes iff phi(m)*sigma(m) 
               = (m-3)*(m+1), where phi(m) = A000010(m) and sigma(m) = A000203(m). 
               Of course, for a product of distinct primes p*q we know sigma(p*q) 
               = (p+1)*(q+1) and if p, q, are twin primes, say q = p + 2, then sigma(p*q) 
               = (p+1)*(q+1) = (p+1)*(p+3). - Jonathan Vos Post (jvospost3(AT)gmail.com), 
               Feb 21 2006
%C A037074 Also the area of twin prime rectangles. A twin prime rectangle is a rectangle 
               whose sides are components of twin prime pairs. E.g. The twin prime 
               pair (3,5) produces a 3x5 unit rectangle which has area 15 square 
               units. - Cino Hilliard (hillcino368(AT)gmail.com), Jul 28 2006
%C A037074 A product of twin primes is of the form 36k^2-1 (cf. A136017, A002822). 
               - Artur Jasinski (grafix(AT)csl.pl), Dec 12 2007
%C A037074 A072965(a(n)) = 1; A072965(m) mod A037074(n) > 0 for all m. - Reinhard 
               Zumkeller (reinhard.zumkeller(AT)gmail.com), Jan 29 2008
%D A037074 Albert A. Mullin, "Bicomposites, twin primes and arithmetic progression", 
               Abstract 04T-11-48, Abstracts of AMS, Vol. 25, No. 4, 2004, p. 795.
%H A037074 T. D. Noe, <a href="b037074.txt">Table of n, a(n) for n=1..10000</a>
%F A037074 a(n) = A001359(n)* A006512(n). A000010(a(n))*A000203(a(n)) = (a(n)-3)*(a(n)+1). 
               - Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 21 2006
%F A037074 a(n)=(A014574(n))^2 - 1. a(n+1)=(6*A002822(n))^2 - 1. - Lekraj Beedassy 
               (blekraj(AT)yahoo.com), Sep 02 2006
%e A037074 a(2)=35 because 5*7=35, that is (5,7) is the 2nd pair of twin primes.
%p A037074 ZL:=[]:for p from 1 to 863 do if (isprime(p) and isprime(p+2) ) then 
               ZL:=[op(ZL),(p*(p+2))]; fi; od; print(ZL); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Mar 07 2007
%p A037074 for i from 1 to 150 do if ithprime(i+1) = ithprime(i) + 2 then print({ithprime(i)*ithprime(i+1)}); 
               fi; od; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 19 2007
%t A037074 s = Select[ Prime@ Range@170, PrimeQ[ # + 2] &]; s(s + 2) (from Robert 
               G. Wilson v (rgwv(at)rgwv.com), Feb 21 2006)
%o A037074 (PARI) g(n) = for(x=1,n,if(prime(x+1)-prime(x)==2,print1(prime(x)*prime(x+1)",
               "))) - Cino Hilliard (hillcino368(AT)gmail.com), Jul 28 2006
%Y A037074 Cf. A000010, A000203, A001359, A006512, A014574.
%Y A037074 Cf. A136017.
%Y A037074 Sequence in context: A070161 A142591 A074480 this_sequence A107423 A027442 
               A074891
%Y A037074 Adjacent sequences: A037071 A037072 A037073 this_sequence A037075 A037076 
               A037077
%K A037074 nice,nonn
%O A037074 1,1
%A A037074 Felice Russo (felice.russo(AT)katamail.com)
%E A037074 More terms from Erich Friedman (erich.friedman(AT)stetson.edu)