A086006 Primes p such that 2*p-1 and 2*p+1 are semiprimes.

17, 43, 47, 61, 71, 101, 107, 109, 151, 197, 223, 317, 349, 421, 461, 521, 569, 631, 673, 701, 821, 881, 919, 947, 971, 991, 1051, 1091, 1109, 1153, 1181, 1217, 1231, 1259, 1321, 1361, 1367, 1549, 1693, 1801, 1847, 1933, 1951, 1979, 2143, 2207

Offset: 1

Author

Reinhard Zumkeller, Jul 07 2003

Keywords

• nonn

Comments

a(n) = A086005(n)/2.

Examples

			101 is prime and 2*101-1=201=3*67, 2*101+1=203=7*29, therefore 101 is a term.
It is the sixth term and a(6)=101=A086005(6)/2.
		

Links

• T. D. Noe, Table of n, a(n) for n=1..10000

Crossrefs

Cf. A001358, A000040.

Programs

Haskell

a086006 = flip div 2 . a086005  -- Reinhard Zumkeller, Aug 08 2013

Mathematica

Select[Prime[Range[400]],PrimeOmega[2#-1]==PrimeOmega[2#+1]==2&] (* Harvey P. Dale, Jun 23 2016 *)

PARI

isok(n) = isprime(n) && (bigomega(2*n+1) == 2) && (bigomega(2*n-1) == 2) \\ Michel Marcus, Aug 01 2013

Formula

A064911(2*a(n)-1) * A064911(2*a(n)+1) = 1. - Reinhard Zumkeller, Aug 08 2013