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

1,1

Comments

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

Links

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

Formula

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

Example

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.

Mathematica

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

Prog

(PARI) isok(n) = isprime(n) && (bigomega(2*n+1) == 2) && (bigomega(2*n-1) == 2) \\ Michel Marcus, Aug 01 2013
(Haskell)
a086006 = flip div 2 . a086005  -- Reinhard Zumkeller, Aug 08 2013

Crossrefs

Cf. A001358, A000040.

Sequence in context: A024188 A196209 A196476 * A195685 A118587 A215164

Adjacent sequences: A086003 A086004 A086005 * A086007 A086008 A086009

Keyword

nonn

Author

Reinhard Zumkeller, Jul 07 2003

Status

approved