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Incrementally largest values of minimal y satisfying the equation x^2 - D*y^2 = -5, where D is a prime number.
2

%I #8 Feb 20 2021 23:09:52

%S 1,3,21,101661,7661007,4799633969721,77198907060727563,

%T 925844015429395821936018843,42098324998788084039841633029,

%U 11083764383781783138639570812583,1490226373435897063030119543467763

%N Incrementally largest values of minimal y satisfying the equation x^2 - D*y^2 = -5, where D is a prime number.

%H Christine Patterson, <a href="/A341086/a341086.txt">COCALC (Sage) Program</a>

%e For D=29, the least positive y for which x^2 - D*y^2 = -5 has a solution is 3. The next prime, D, for which x^2 - D*y^2 = -5 has a solution is 41, but the smallest positive y in this case is 1, which is less than the previous record y, 3. So, 41 is not a term.

%e The next prime, D, after 41 for which x^2 - D*y^2 = -5 has a solution is 61 and the least positive y for which it has a solution is y=21, which is larger than 3, so it is a new record y value. So 61 is a term of A341085 and 21 is a term of this sequence.

%Y Cf. A033315, A341085.

%K nonn

%O 1,2

%A _Christine Patterson_, Feb 13 2021

%E a(1)=1 inserted and Example edited by _Jon E. Schoenfield_, Feb 20 2021