A356048 a(n) is the least prime p such that p^2 - 2*prime(n)^2 is prime.

5, 5, 11, 11, 17, 19, 29, 31, 37, 43, 53, 53, 61, 61, 67, 101, 97, 89, 97, 107, 109, 131, 127, 131, 139, 151, 149, 163, 157, 163, 181, 193, 199, 197, 227, 223, 223, 233, 257, 263, 263, 271, 271, 281, 293, 283, 317, 317, 347, 331, 331, 349, 349, 359, 367, 379, 389, 409, 431, 401, 409, 419, 449

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

a(n)^2 = 2*A001248(n) + A356060(n).

Example

a(3) = 11 because 11 is prime, the third prime is 5, 11^2-2*5^2 = 71 is prime, and 11 is the least prime that works.

Maple

f:= proc(n) local q;
    q:= floor(sqrt(2)*n);
    do
      q:= nextprime(q);
      if isprime(q^2-2*n^2) then return q fi;
    od
end proc:
map(f, [seq(ithprime(i), i=1..100)]);

Mathematica

a[n_] := Module[{m = 2*Prime[n]^2, p}, p = Floor[Sqrt[m]]; While[p = NextPrime[p]; !PrimeQ[p^2 - m]]; p]; Array[a, 100] (* Amiram Eldar, Jul 24 2022 *)

Prog

(Python)
from sympy import isprime, nextprime, prime
def a(n):
    p = pn = prime(n)
    while not isprime(p*p - 2*pn*pn): p = nextprime(p)
    return p
print([a(n) for n in range(1, 64)]) # Michael S. Branicky, Jul 24 2022

Crossrefs

Cf. A001248, A356060.

Sequence in context: A239355 A218121 A168300 * A101203 A141244 A121849

Adjacent sequences: A356045 A356046 A356047 * A356049 A356050 A356051

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Jul 24 2022

Status

approved