A304903 Least prime p such that 2*n^2 - p is prime.

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, 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, 3, 7, 31, 7, 5, 13, 3, 5

Offset: 2

Author

Hugo Pfoertner, May 20 2018

Keywords

• nonn

Comments

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.

Examples

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

Crossrefs

Cf. A304874, A304875, A304904, A304905.

Programs

Mathematica

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 *)

PARI

a(n) = forprime(p=3, , if(ispseudoprime(2*n^2-p), return(p))) \\ Felix Fröhlich, May 20 2018

Formula

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