

A104163


Primes p such that (2p+1)/3 is prime.


4



7, 19, 43, 61, 79, 109, 151, 163, 223, 271, 349, 421, 439, 523, 601, 613, 631, 673, 691, 811, 853, 919, 991, 1009, 1051, 1063, 1153, 1213, 1231, 1279, 1321, 1429, 1531, 1549, 1663, 1693, 1789, 1801, 1873, 1933, 1951, 2113, 2143, 2179, 2221, 2239, 2503, 2539
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OFFSET

1,1


COMMENTS

Dickson's conjecture implies that this sequence is infinite.  Charles R Greathouse IV, Jul 31 2012


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000


FORMULA

a(n)=(3*A158708(n+1)1)/2 Zak Seidov, Jul 31 2012


EXAMPLE

7 is in the sequence because (2 * 7 + 1)/3 = 5, which is also prime.
19 is in the sequence because (2 * 19 + 1)/3 = 13, which is also prime.


MATHEMATICA

Select[Range[7, 2539, 2], PrimeQ[#] && PrimeQ[(2# + 1)/3]&] (* Zak Seidov, Jul 31 2012 *)
Select[Prime[Range[400]], PrimeQ[(2 # + 1) / 3]&] (* Vincenzo Librandi, Apr 14 2013 *)


PROG

(PARI) is(n)=n%3==1 && isprime((2*n+1)/3) && isprime(n) \\ Charles R Greathouse IV, Jul 31 2012


CROSSREFS

Cf. A005384.
Sequence in context: A225279 A192755 A141193 * A145993 A265676 A054690
Adjacent sequences: A104160 A104161 A104162 * A104164 A104165 A104166


KEYWORD

nonn,easy


AUTHOR

Roger L. Bagula, Mar 10 2005


EXTENSIONS

New name from Charles R Greathouse IV, Jul 31 2012


STATUS

approved



