A257789 Numbers n such that 2n*prime(n) - 1 and 2n*prime(n) + 1 are both prime.

1, 2, 3, 24, 30, 33, 54, 90, 156, 168, 189, 225, 294, 300, 402, 576, 741, 780, 825, 849, 918, 948, 978, 1014, 1245, 1542, 1551, 1608, 1614, 1617, 1770, 1773, 1908, 1914, 1920, 1947, 2025, 2286, 2361, 2370, 2598, 2760, 2865, 2970, 3081, 3516, 3744, 3759, 3948, 4023

Offset: 1

Author

Juri-Stepan Gerasimov, May 08 2015

Keywords

• nonn
• easy

Comments

a(n) is divisible by 3 for n >= 3. - Robert Israel, May 08 2015

Examples

			2 is in this sequence because 2*2*prime(2) - 1 = 11 and 2*2*prime(2) + 1 = 13 are both prime.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A085637.

Programs

Magma

[n: n in [1..4500] | IsPrime(2*n*NthPrime(n)-1) and IsPrime(2*n*NthPrime(n)+1)];

Maple

filter:= proc(n)
local p;
p:= ithprime(n);
isprime(2*n*p+1) and isprime(2*n*p-1)
end proc:
select(filter, [1,2,seq(3*j,j=1..10^5)]); # Robert Israel, May 08 2015

Mathematica

Select[Range[3000], PrimeQ[2 # Prime[#] - 1] && PrimeQ[2 #  Prime[#] + 1] &] (* Vincenzo Librandi, May 09 2015 *)
Select[Range[4200],AllTrue[2# Prime[#]+{1,-1},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Dec 08 2018 *)

PARI

v=List(); n=0; forprime(p=2,1e5, n++; if(isprime(2*n*p-1) && isprime(2*n*p+1), listput(v,n))); Vec(v) \\ Charles R Greathouse IV, May 08 2015