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A173084 Semiprimes q such that q^2-4 and q^2+4 are also semiprimes. 4
9, 21, 69, 129, 381, 2271, 3849, 3909, 3921, 5001, 5079, 5169, 5349, 7041, 16251, 18129, 18399, 20481, 22569, 22641, 22719, 22809, 28029, 32259, 35151, 38559, 39021, 39441, 39981, 41079, 42459, 48759, 48819, 49431, 50649, 61629, 67929 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

From Robert Israel, Jun 01 2018: (Start)

Since q^2-4 = (q-2)(q+2), for this to be a semiprime requires q-2 and q+2 to be primes.

All terms == 3 (mod 6), thus q/3 is an odd prime. (End)

LINKS

Robert Israel, Table of n, a(n) for n = 1..2365

EXAMPLE

9^2-4 = 77 = 7*11 and 9^2+4 = 85 = 5*13 are semiprimes created by q=9, which adds the semiprime q=9 to the sequence.

MAPLE

N:= 10^5: # to get all terms <= N

P:= select(isprime, [seq(i, i=3..N/3, 2)]):

select(q -> isprime(q-2) and isprime(q+2) and numtheory:-bigomega(q^2+4)=2, 3*P); # Robert Israel, Jun 01 2018

MATHEMATICA

f[n_]:=Last/@FactorInteger[n]=={1, 1}||Last/@FactorInteger[n]=={2}; lst={}; Do[If[f[n], a=n^2-4; b=n^2+4; If[f[a]&&f[b], AppendTo[lst, n]]], {n, 9!}]; lst

PROG

IsSemiprime:=func<n | &+[d[2]: d in Factorization(n)] eq 2>; [n: n in [4..7*10^4] | IsSemiprime(n) and IsSemiprime(n^2+4) and IsSemiprime(n^2-4)]; // Vincenzo Librandi, Jun 02 2018

CROSSREFS

Cf. A001358, A173082, A173083

Sequence in context: A147466 A262055 A193276 * A137340 A075640 A147480

Adjacent sequences:  A173081 A173082 A173083 * A173085 A173086 A173087

KEYWORD

nonn

AUTHOR

Vladimir Joseph Stephan Orlovsky, Feb 09 2010

EXTENSIONS

Definition reworded by R. J. Mathar, Mar 14 2010

STATUS

approved

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Last modified September 16 06:21 EDT 2019. Contains 327090 sequences. (Running on oeis4.)