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%I #17 Jan 02 2022 14:07:32
%S 1,3,13,59,221,8807,527593,52778687,113759383,13458244873,
%T 313074529583,1434867510253,30909266676193,842239594152347,
%U 1075672117707143,29204057639975683,52376951398984393,4785745078256208692917,15280437983663153103594943
%N Incrementally largest values of minimal x satisfying the equation x^2 - D*y^2 = -2, where D is an odd prime number.
%C Analogous to A033315 for x^2-D*y^2=1, and D required to be prime.
%H Christine Patterson, <a href="/A336791/a336791.txt">Cocalc (Sage) program</a>
%e 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.
%t 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 *)
%Y Cf. A033315, A336790.
%K nonn
%O 1,2
%A _Christine Patterson_, Oct 14 2020
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