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A336791
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Incrementally largest values of minimal x satisfying the equation x^2 - D*y^2 = -2, where D is an odd prime number.
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2
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1, 3, 13, 59, 221, 8807, 527593, 52778687, 113759383, 13458244873, 313074529583, 1434867510253, 30909266676193, 842239594152347, 1075672117707143, 29204057639975683, 52376951398984393, 4785745078256208692917, 15280437983663153103594943
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OFFSET
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1,2
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COMMENTS
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Analogous to A033315 for x^2-D*y^2=1, and D required to be prime.
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LINKS
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EXAMPLE
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For D=43, the least x for which x^2-D*y^2=-2 has a solution is 59. The next prime, D, for which x^2-D*y^2=-2 has a solution is 59, but the smallest x in this case is 23, which is less than 59. The next prime, D, after 59 for which x^2-D*y^2=-2 has a solution is 67 and the least x for which it has a solution is 221, which is larger than 59, so it is a new record value. 67 is a term of A336790 and 221 is a term of this sequence, but 59 is not a term of A336790 because the least x for which x^2-47*y^2=-2 has a solution at D=59 is not a record value.
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MATHEMATICA
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records[n_]:=Module[{ri=n, m=0, rcs={}, len}, len=Length[ri]; While[ len>0, If[ First[ri]>m, m=First[ri]; AppendTo[rcs, m]]; ri=Rest[ri]; len--]; rcs]; records[ Abs[Flatten[Table[x/.FindInstance[x^2-p y^2==-2, {x, y}, Integers], {p, Prime[Range[2, 500]]}]/.x->Nothing]]] (* Harvey P. Dale, Jan 02 2022 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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