A271653 Primes of the form 2*prime(2k) - prime(k).
11, 31, 47, 61, 113, 127, 179, 241, 307, 419, 433, 449, 491, 853, 881, 1063, 1153, 1201, 1289, 1487, 1823, 1997, 2011, 2027, 2333, 2441, 2459, 2647, 2851, 2927, 3041, 3449, 3491, 3853, 4057, 4241, 4259, 4397, 4423, 4679, 4721, 5003, 5179, 5233, 5569, 5653, 5867, 6397, 6481, 6661
Offset: 1
Keywords
Examples
For n=1, 2*prime(2*2)-prime(2) = 2*7-3 = 11 is prime when k=2. For n=2, 2*prime(2*4)-prime(4) = 2*19-7 = 31 is prime when k=4.
Crossrefs
Cf. A272042.
Programs
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Magma
[a: n in [0..400] | IsPrime(a) where a is 2*NthPrime(2*n) - NthPrime(n)]; // Vincenzo Librandi, Apr 15 2016
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Maple
A271653:=n->`if`(isprime(2*ithprime(2*n)-ithprime(n)), 2*ithprime(2*n)-ithprime(n), NULL): seq(A271653(n), n=1..600); # Wesley Ivan Hurt, Apr 17 2016
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Mathematica
Select[Table[2*Prime[2 k] - Prime[k], {k, 0, 100}], PrimeQ] -
PARI
lista(nn) = for(n=1, nn, if(isprime(p=2*prime(2*n)-prime(n)), print1(p, ", "))); \\ Altug Alkan, Apr 13 2016