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Value of prime number D for incrementally largest values of minimal y satisfying the equation x^2-D*y^2=5.
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%I #8 Feb 14 2021 13:24:37

%S 19,61,149,241,409,421,541,1069,1249,1381,1621,4261,4621,4789,6301,

%T 8269,12601,12721,14449,16069,20101,32029,33889,34381,35281,38329,

%U 43261,45061,60589,87481,89989,97549,99661,121081,125101,166021,178621,187069,191689,202381

%N Value of prime number D for incrementally largest values of minimal y satisfying the equation x^2-D*y^2=5.

%H Christine Patterson, <a href="/A341081/a341081.txt">COCALC (Sage) Program</a>

%e For D=19, the least positive y for which x^2-D*y^2=5 has a solution is 2. The next prime, D, for which x^2-D*y^2=5 has a solution is 29, but the smallest positive y in this case is 2, which is equal to the previous record y. So, 29 is not a term.

%e The next prime, D, after 19 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=58, which is larger than 2, so it is a new record y value. So 61 is in this sequence and 58 is in A341082.

%Y Cf. A033316 (analogous for x^2-D*y^2=1), A341079 (similar sequence for x's), A341082.

%K nonn

%O 1,1

%A _Christine Patterson_, Feb 13 2021