OFFSET
1,1
COMMENTS
REFERENCES
J.-R. Chen, On the representation of a large even integer as the sum of a prime and a product of at most two primes, Sci. Sinica 16 (1973), 157-176.
LINKS
K. D. Bajpai,Table of n, a(n) for n = 1..14190(first 1000 terms from T. D. Noe)
P. Pollack,Analytic and Combinatorial Number TheoryCourse Notes, p. 146. [?Broken link]
P. Pollack,Analytic and Combinatorial Number TheoryCourse Notes, p. 146.
T. Tao,Obstructions to uniformity and arithmetic patterns in the primes,arXiv:math/0505402 [math.NT], 2005.
FORMULA
a(n) =A062721(n) - 2.
EXAMPLE
FromK. D. Bajpai,Sep 06 2014: (Start)
a(3) = 13, which is prime, and 13 + 2 = 15 = 3 * 5, which is a semiprime.
a(4) = 19, which is prime, and 19 + 2 = 21 = 3 * 7, which is a semiprime.
(End)
MAPLE
select(t -> isprime(t) and numtheory:-bigomega(t+2)=2, [2, seq(2*i+1, i=1..500)]); #Robert Israel,Sep 07 2014
MATHEMATICA
f[n_]:= Plus @@ Flatten[ Table[ # [[2]], {1}] & /@ FactorInteger[ n]]; Select[ Prime[ Range[ 123]], f[ # + 2] == 2 &] (*Robert G. Wilson v,Apr 30 2005 *)
Select[Prime[Range[500]], PrimeOmega[#+2]==2&] (*K. D. Bajpai,Sep 06 2014 *)
PROG
(PARI) { n=0; for (m=1, 10^9, p=prime(m); if (bigomega(p + 2) == 2, write( "b063637.txt", n++, "", p); if (n==1000, break)) ) } \\Harry J. Smith,Aug 26 2009
(Haskell)
a063637 n = a063637_list!!(n-1)
a063637_list = filter ((== 1). a064911. (+ 2)) a000040_list
--Reinhard Zumkeller,Nov 15 2011
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller,Jul 21 2001
STATUS
approved