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

1,3

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

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 *)

Crossrefs

Sequence in context: A274198 A002079 A006126 * A225432 A086382 A249416

Adjacent sequences: A078354 A078355 A078356 * A078358 A078359 A078360

Keyword

nonn

Author

Wolfdieter Lang, Nov 29 2002

Extensions

Edited and extended by Max Alekseyev, Mar 03 2010

Status

approved