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Search: id:A082394
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| A082394 |
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Let p = n-th prime of the form 4k+3, take smallest solution (x,y) to the Pellian equation x^2 - p*y^2 = 1 with x and y >= 1; sequence gives value of y. |
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3
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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
(list; graph; listen)
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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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Cino Hilliard, 8 divides n^2-1 for odd n
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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]] (from Robert G. Wilson v Sep 02 2004)
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PROGRAM
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(PARI) p4xp3(n, m) = { forstep(p=3, m, 4, for(x=1, n, if(isprime(p), y=x*x*p+1; if(issquare(y), print1(x" "); break; ) ) ) ) }
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CROSSREFS
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Values of x are in A081231. Equals A002349(p). Cf. A082393.
Sequence in context: A086667 A067098 A088060 this_sequence A086889 A059495 A083391
Adjacent sequences: A082391 A082392 A082393 this_sequence A082395 A082396 A082397
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KEYWORD
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easy,nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), Apr 14 2003
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 15 2003; recomputed Sep 03 2004
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