login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A218046 Primes p such that 8p + 2r is a primorial for some r in A006512. 2
2, 11, 23, 83, 113, 131, 173, 191, 233, 239, 251, 263, 281, 293, 359, 419, 431, 449, 503, 641, 653, 659, 701, 719, 743, 761, 809, 821, 881, 911, 953, 1013, 1019, 1031, 1049, 1103, 1223, 1229, 1289, 1301, 1433, 1439, 1451, 1493, 1511, 1559, 1583, 1601, 1619 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The primes p in this sequence satisfy b#/2 = 4p + r,  where p is a prime, b# is a primorial, and r is the second of the twin prime pair (r-2, r).

Each p is therefore associated with at least one primorial, and with a pair of twin primes.

The empirical evidence suggests that each twin prime pair is associated with at least one p, and each p with a twin prime pair. I conjecture that this sequence (and therefore the sequence of twin primes) is infinite.

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..354

Michael Kaarhus, Twin Prime Conjectures 1, 2 and 3, 2012, (PDF)

EXAMPLE

8*2   + 2*7 = 5#

8*11  + 2*61 = 7#

8*23  + 2*13 = 7#

8*83  + 2*823 = 11#

8*113 + 2*14563 = 13#

8*131 + 2*254731 = 17#

8*173 + 2*463 = 11#

8*191 + 2*14251 = 13#

8*233 + 2*14083 = 13#

8*239 + 2*199 = 11#

8*251 + 2*151 = 11#

8*263 + 2*103 = 11#

8*281 + 2*31 = 11#

8*293 + 2*307444891294244533 = 47#

8*359 + 2*253819 = 17#

PROG

(PARI) list(lim)={

    my(v=List(), P=3, q);

    forprime(p=5, lim,

        P*=p;

        forprime(t=2, min(lim, (P-2)\4),

            q=P-4*t;

            if(q%6==1 && ispseudoprime(q) && ispseudoprime(q-2), listput(v, t))

        )

    );

    vecsort(Vec(v), , 8)

}; \\ Charles R Greathouse IV, Oct 23 2012

CROSSREFS

Sequence in context: A141423 A106974 A198277 * A217309 A115374 A078699

Adjacent sequences:  A218043 A218044 A218045 * A218047 A218048 A218049

KEYWORD

nonn

AUTHOR

Michael G. Kaarhus, Oct 19 2012

EXTENSIONS

Terms corrected by Charles R Greathouse IV, Oct 23 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 25 12:04 EDT 2019. Contains 322456 sequences. (Running on oeis4.)