A365241 a(n) is the n-th prime of the form 2*n + k where k > 0.

3, 7, 13, 19, 23, 31, 41, 43, 53, 61, 67, 73, 79, 83, 97, 103, 107, 109, 127, 131, 139, 151, 157, 167, 173, 179, 191, 193, 197, 211, 227, 229, 233, 241, 251, 263, 271, 277, 281, 293, 307, 313, 317, 331, 347, 349, 353, 359, 373, 379, 389, 401, 409, 421, 433, 439

Offset: 1

Author

Tamas Sandor Nagy, Aug 28 2023

Keywords

• nonn

Examples

			a(3) = 13 because at k = 1, 2 * 3 + 1 = 7, this being the first prime result of the sum. At k = 2, the sum is 8, which is not a prime, so trying incremental k's, the second prime 11 is found with k = 5. The third prime at n = 3 and k = 7 is found to be 13, therefore a(3) = 13.
		

Crossrefs

Cf. A000040, A060264.

Programs

Maple

f:= proc(n)
      ithprime(numtheory:-pi(2*n)+n)
end proc:
map(f, [$1..100]); # Robert Israel, Aug 28 2023

Mathematica

a[n_] := NextPrime[2*n, n]; Array[a, 60] (* Amiram Eldar, Aug 28 2023 *)

PARI

a(n) = prime(primepi(2*n) + n) \\ David A. Corneth, Aug 28 2023 after Jon E. Schoenfield

PARI

first(n) = {my(res = vector(n), ind = 1, nextpp = 2, pp = 2); forprime(p = 3, oo, if(pp >= nextpp, res[ind] = p;if(isprime(2*ind+1), nextpp+=2,nextpp+=1);ind++;if(ind > n,return(res))); pp++;)} \\ David A. Corneth, Aug 28 2023