A336791 Incrementally largest values of minimal x satisfying the equation x^2 - D*y^2 = -2, where D is an odd prime number.
1, 3, 13, 59, 221, 8807, 527593, 52778687, 113759383, 13458244873, 313074529583, 1434867510253, 30909266676193, 842239594152347, 1075672117707143, 29204057639975683, 52376951398984393, 4785745078256208692917, 15280437983663153103594943
Offset: 1
Keywords
Examples
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.
Links
- Christine Patterson, Cocalc (Sage) program
Programs
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Mathematica
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 *)
Comments