A078357 Minimal positive solution x of Pell equation y^2 - A077426(n)*x^2 = -4.

1, 1, 2, 1, 2, 10, 1, 5, 2, 250, 1, 106, 1138, 2, 25, 146, 1, 298, 2, 5, 17, 1, 97, 10, 253970, 2, 1, 3034, 9148450, 2, 746, 10, 157, 126890, 1, 14341370, 5, 2, 110671282, 986, 7586, 1, 530, 130, 173, 2, 11068353370, 21685, 26, 694966754, 1, 17883410, 5528222698, 17, 87922, 2, 5, 41

Offset: 1

Author

Wolfdieter Lang, Nov 29 2002

Keywords

• nonn

Comments

The corresponding values y are given in A078356.

For the general solution of Pell equation y^2 - A077426(n)*x^2 = -4 see a comment in A078356.

For the conversion of the values given in Perron's table to sequences A078356 and A078357, see comments in A078356.

References

• O. Perron, "Die Lehre von den Kettenbruechen, Bd.I", Teubner, 1954, 1957 (Sec. 30, Satz 3.35, p. 109 and table p. 108).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..120

Programs

Mathematica

$MaxExtraPrecision = 100; A077426 = Select[Range[ 600], ! IntegerQ[Sqrt[#]] && OddQ[ Length[ ContinuedFraction[(Sqrt[#] + 1)/2] // Last]] &]; a[n_] := {y, x} /. {ToRules[ Reduce[y > 0 && x > 0 && y^2 - A077426[[n]]*x^2 == -4, {y, x}, Integers] /. C[1] -> 0]} // Sort // First // Last; Table[a[n], {n, 1, 60}] (* Jean-François Alcover, Jun 21 2013 *)

Extensions

Edited and extended by Max Alekseyev, Mar 03 2010