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A082394
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Let p = n-th prime of the form 4k+3, take the solution (x,y) to the Pellian equation x^2 - p*y^2 = 1 with x and smallest y >= 1; sequence gives value of y.
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6
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1, 3, 3, 39, 5, 273, 531, 7, 69, 5967, 413, 9, 9, 22419, 93, 419775, 927, 6578829, 140634693, 5019135, 13, 313191, 650783, 1153080099, 19162705353, 15, 15, 400729, 231957, 8579, 7044978537, 8219541, 5052633, 957397, 153109862634573, 34443, 19
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OFFSET
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1,2
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REFERENCES
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C. Stanley Ogilvy, Tomorrow's Math, 1972, p. 119.
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LINKS
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EXAMPLE
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For n=3, p = 11, x=10, y=3 since we have 10^2 = 11*3^2 + 1, so a(3) = 3.
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MATHEMATICA
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PellSolve[(m_Integer)?Positive] := Module[{cf, n, s}, cf = ContinuedFraction[ Sqrt[m]]; n = Length[ Last[cf]]; If[ OddQ[n], n = 2*n]; s = FromContinuedFraction[ ContinuedFraction[ Sqrt[m], n]]; {Numerator[s], Denominator[s]}]; Transpose[ PellSolve /@ Select[ Prime[ Range[72]], Mod[ #, 4] == 3 &]][[2]] (* Robert G. Wilson v, Sep 02 2004 *)
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PROG
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(PARI) p4xp3(n, m) = { forstep(p=3, m, 4, for(y=1, n, if(isprime(p), x=y*y*p+1; if(issquare(x), print1(y" "); break; ) ) ) ) }
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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