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A086006 Primes p such that 2*p-1 and 2*p+1 are semiprimes. 9
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 20 14:23 EDT 2019. Contains 325185 sequences. (Running on oeis4.)