login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A063637 Primes p such that p+2 is a semiprime. 16
2, 7, 13, 19, 23, 31, 37, 47, 53, 67, 83, 89, 109, 113, 127, 131, 139, 157, 167, 181, 199, 211, 233, 251, 257, 263, 293, 307, 317, 337, 353, 359, 379, 389, 401, 409, 443, 449, 467, 479, 487, 491, 499, 503, 509, 541, 557, 563, 571, 577, 587, 631, 647, 653, 677 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Primes of form p*q - 2, where p and q are primes.

Union of A049002 and A115093. - T. D. Noe, Mar 01 2006

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

T. D. Noe and 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 Theory Course Notes, p. 146. [?Broken link]

P. Pollack, Analytic and Combinatorial Number Theory Course 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.

A010051(a(n)) * A064911(a(n) + 2) = 1. [Reinhard Zumkeller, Nov 15 2011]

EXAMPLE

From K. D. Bajpai, Sep 06 2014: (Start)

a(3) = 13, that is prime. 13 + 2 = 15 = 3 * 5, which is a semiprime.

a(4) = 19, that is prime. 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

Cf. A005383, A001358, A063638.

Cf. A109611 (Chen primes).

Sequence in context: A007821 A156007 A067774 * A216526 A020623 A109346

Adjacent sequences:  A063634 A063635 A063636 * A063638 A063639 A063640

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Jul 21 2001

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified November 27 17:39 EST 2014. Contains 250249 sequences.