A344463 - OEIS

%I #8 May 20 2021 22:58:20

%S 2,0,239,251,2069,131,521,0,2243,379,643,40849,89101,11717,81839,

%T 18787,659,0,2887,41081,199261,13931,4231,223439,17443,953,3499,6689,

%U 122131,298777,9883,0,93131,12329,48989,67307,9199,44549,13903,294353,605071,42331,7309,167677,41651,46747,129581

%N a(n) is the least prime p such that (p^2-2*n)/(2*n-1) and (p^2+2*n)/(2*n+1) are both prime, or 0 if such p does not exist.

%C a(n) = 0 if 2*n is a square.

%H Robert Israel, <a href="/A344463/b344463.txt">Table of n, a(n) for n = 1..10000</a>

%e a(3) = 239 because 239, (239^2-2*3)/(2*3-1) = 11423, and (239^2+2*3)/(2*3+1) = 8161 are primes, and no smaller prime works.

%p f:= proc(n) local M,p,i,j;

%p   if issqr(2*n) then return 0 fi;

%p   M:= sort(map(t -> rhs(op(t)), [msolve(p^2=1,4*n^2-1)]));

%p   for i from 0 to 10^6 do

%p     for j in M do

%p       p:= i*(4*n^2-1)+j;

%p       if isprime(p) and isprime((p^2-2*n)/(2*n-1)) and  isprime((p^2+2*n)/(2*n+1)) then return p fi

%p   od od;

%p   FAIL

%p end proc:

%p map(f, [$1..100]);

%Y Cf. A001105.

%K nonn

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, May 19 2021