A257789 - OEIS

%I #21 Sep 08 2022 08:46:12

%S 1,2,3,24,30,33,54,90,156,168,189,225,294,300,402,576,741,780,825,849,

%T 918,948,978,1014,1245,1542,1551,1608,1614,1617,1770,1773,1908,1914,

%U 1920,1947,2025,2286,2361,2370,2598,2760,2865,2970,3081,3516,3744,3759,3948,4023

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

%C a(n) is divisible by 3 for n >= 3. - _Robert Israel_, May 08 2015

%H Charles R Greathouse IV, <a href="/A257789/b257789.txt">Table of n, a(n) for n = 1..10000</a>

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

%p filter:= proc(n)

%p local p;

%p p:= ithprime(n);

%p isprime(2*n*p+1) and isprime(2*n*p-1)

%p end proc:

%p select(filter, [1,2,seq(3*j,j=1..10^5)]); # _Robert Israel_, May 08 2015

%t Select[Range[3000], PrimeQ[2 # Prime[#] - 1] && PrimeQ[2 #  Prime[#] + 1] &] (* _Vincenzo Librandi_, May 09 2015 *)

%t 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 *)

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

%o (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

%Y Cf. A085637.

%K nonn,easy

%O 1,2

%A _Juri-Stepan Gerasimov_, May 08 2015