1,1

Except for the first term, all entries have digital root 8. - Lekraj Beedassy (blekraj(AT)yahoo.com), Jun 11 2004

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

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

A product of twin primes is of the form 36k^2-1 (cf. A136017, A002822). - Artur Jasinski (grafix(AT)csl.pl), Dec 12 2007

A072965(a(n)) = 1; A072965(m) mod A037074(n) > 0 for all m. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jan 29 2008

Albert A. Mullin, "Bicomposites, twin primes and arithmetic progression", Abstract 04T-11-48, Abstracts of AMS, Vol. 25, No. 4, 2004, p. 795.

T. D. Noe, Table of n, a(n) for n=1..10000

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

a(n)=(A014574(n))^2 - 1. a(n+1)=(6*A002822(n))^2 - 1. - Lekraj Beedassy (blekraj(AT)yahoo.com), Sep 02 2006

a(2)=35 because 5*7=35, that is (5,7) is the 2nd pair of twin primes.

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

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

s = Select[ Prime@ Range@170, PrimeQ[ # + 2] &]; s(s + 2) (from Robert G. Wilson v (rgwv(at)rgwv.com), Feb 21 2006)

(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

Cf. A000010, A000203, A001359, A006512, A014574.

Cf. A136017.

Sequence in context: A070161 A142591 A074480 this_sequence A107423 A027442 A074891

Adjacent sequences: A037071 A037072 A037073 this_sequence A037075 A037076 A037077

nice,nonn

Felice Russo (felice.russo(AT)katamail.com)

More terms from Erich Friedman (erich.friedman(AT)stetson.edu)