A356048 - OEIS

%I #14 Jul 25 2022 09:13:24

%S 5,5,11,11,17,19,29,31,37,43,53,53,61,61,67,101,97,89,97,107,109,131,

%T 127,131,139,151,149,163,157,163,181,193,199,197,227,223,223,233,257,

%U 263,263,271,271,281,293,283,317,317,347,331,331,349,349,359,367,379,389,409,431,401,409,419,449

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

%H Robert Israel, <a href="/A356048/b356048.txt">Table of n, a(n) for n = 1..10000</a>

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

%e 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.

%p f:= proc(n) local q;

%p     q:= floor(sqrt(2)*n);

%p     do

%p       q:= nextprime(q);

%p       if isprime(q^2-2*n^2) then return q fi;

%p     od

%p end proc:

%p map(f, [seq(ithprime(i),i=1..100)]);

%t 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 *)

%o (Python)

%o from sympy import isprime, nextprime, prime

%o def a(n):

%o     p = pn = prime(n)

%o     while not isprime(p*p - 2*pn*pn): p = nextprime(p)

%o     return p

%o print([a(n) for n in range(1, 64)]) # _Michael S. Branicky_, Jul 24 2022

%Y Cf. A001248, A356060.

%K nonn

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Jul 24 2022