A304903 - OEIS

%I #13 May 20 2018 18:02:59

%S 3,5,3,3,5,19,19,5,3,3,5,7,3,7,3,7,5,3,3,5,31,7,23,13,31,5,19,13,11,

%T 43,19,17,3,3,13,7,31,5,13,3,11,7,19,23,3,61,5,3,7,5,61,37,5,3,3,7,19,

%U 3,7,31,7,5,13,3,5

%N Least prime p such that 2*n^2 - p is prime.

%C Each square > 1 can be written as the average of 2 primes p1 < p2. a(n) gives the least prime p1 such that n^2 = (p1 + p2) / 2. The corresponding p2 is provided in A304904.

%F a(n) = n^2 - A304905(n) = A304904(n) - 2*A304905(n).

%e a(5) = 3 because 2*5^2 - 3 = 47 is prime,

%e a(7) = 19 because 2*7^2 - 19 = 71 is prime, whereas all of 98 - 3 = 95, 98 - 5 = 93, 98 - 7 = 91, 98 - 11 = 87, 98 - 13 = 85 and 98 - 17 = 81 are composite.

%t f[n_] := Block[{p = 2}, While[ !PrimeQ[2 n^2 - p], p = NextPrime@ p]; p]; Array[f, 65, 2] (* _Robert G. Wilson v_, May 20 2018 *)

%o (PARI) a(n) = forprime(p=3, , if(ispseudoprime(2*n^2-p), return(p))) \\ _Felix Fröhlich_, May 20 2018

%Y Cf. A304874, A304875, A304904, A304905.

%K nonn

%O 2,1

%A _Hugo Pfoertner_, May 20 2018