A336793 - OEIS

A336793

Incrementally largest values of minimal positive y satisfying the equation x^2 - D*y^2 = -2, where D is an odd prime number.

%I #18 Feb 13 2021 23:08:07

%S 1,3,9,27,747,36321,2900979,5843427,563210019,11516632737,48957047673,

%T 953426773899,23440805582361,27491112569139,734940417828177,

%U 1270701455204457,106719437154440984241,292398373544007804918339,62392836359922644036329593,607918712560763608313068257

%N Incrementally largest values of minimal positive y satisfying the equation x^2 - D*y^2 = -2, where D is an odd prime number.

%C For the corresponding numbers D see A336792.

%H Christine Patterson, <a href="/A336793/a336793.txt">Sage Program</a>

%e For D=3, the least positive y for which x^2-D*y^2=-2 has a solution is 1. The next prime, D, for which x^2-D*y^2=-2 has a solution is 11, but the smallest positive y in this case is also 1, which is equal to the previous record y. So 11 is not a term.

%e The next prime, D, after 11 for which x^2-D*y^2=-2 has a solution is 19 and the least positive y for which it has a solution is y=3, which is larger than 1, so it is a new record y value. So 19 is a term of A336792 and 3 is a term of this sequence.

%Y Cf. A033315, A336792.

%K nonn

%O 1,2

%A _Christine Patterson_, Oct 14 2020