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

1,2

Comments

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

Links

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A085637.

Sequence in context: A037319 A032811 A092049 * A377825 A336616 A354278

Adjacent sequences: A257786 A257787 A257788 * A257790 A257791 A257792

Keyword

nonn,easy

Author

Juri-Stepan Gerasimov, May 08 2015

Status

approved