|
|
A063637
|
|
Primes p such that p+2 is a semiprime.
|
|
19
|
|
|
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 the form p*q - 2, where p and q are primes.
|
|
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
|
|
|
FORMULA
|
|
|
EXAMPLE
|
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
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|