A234095 Primes p such that 2*p + 1 is semiprime.

7, 17, 19, 43, 47, 59, 61, 71, 79, 101, 107, 109, 149, 151, 163, 167, 197, 223, 257, 263, 271, 311, 317, 347, 349, 353, 383, 389, 401, 421, 439, 449, 461, 479, 503, 521, 523, 557, 569, 599, 601, 613, 631, 673, 677, 691, 701, 811, 821, 827, 839, 853, 863, 881

Offset: 1

Author

Clark Kimberling, Dec 27 2013

Keywords

• nonn
• easy

Comments

Also primes of the form (p*q - 1)/2, where p and q are distinct primes.

Examples

			7 is in the sequence because it is prime and 7*2 + 1 = 15 = 3*5 is a semiprime.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A233561, A234096, A233562.

Programs

Magma

IsSemiprime:=func< p | &+[ k[2]: k in Factorization(p)] eq 2 >; [p: p in PrimesUpTo(1000)| IsSemiprime(2*p+1)]; // Vincenzo Librandi, Feb 21 2014

Mathematica

t = Select[Range[1, 7000, 2], Map[Last, FactorInteger[#]] == Table[1, {2}] &]; Take[(t - 1)/2, 120] (* A234093 *)
v = Flatten[Position[PrimeQ[(t - 1)/2], True]] ; w = Table[t[[v[[n]]]], {n, 1, Length[v]}]  (* A233561 *)
(w - 1)/2 (* A234095 *)  (* Peter J. C. Moses, Dec 23 2013 *)
Select[Prime[Range[200]],PrimeOmega[2#+1]==2&] (* Harvey P. Dale, Mar 19 2015 *)

PARI

is(n)=isprime(n) && bigomega(2*n+1)==2 \\ Charles R Greathouse IV, Feb 19 2014

Formula

2*a(n)+1 = A233561(n). - R. J. Mathar, Aug 30 2016

Extensions

New name from Zak Seidov, Feb 19 2014