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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

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OFFSET

1,1

COMMENTS

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

LINKS

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

FORMULA

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

EXAMPLE

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

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 *)

PROG

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

(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

CROSSREFS

Cf. A233561, A234096, A233562.

Sequence in context: A156011 A155774 A180641 * A354168 A287182 A104480

Adjacent sequences: A234092 A234093 A234094 * A234096 A234097 A234098

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Dec 27 2013

EXTENSIONS

New name from Zak Seidov, Feb 19 2014

STATUS

approved

URL: https://oeis.org/A234095

⇱ A234095 - OEIS