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 A078357 Minimal positive solution x of Pell equation y^2 - A077426(n)*x^2 = -4. 8
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified April 18 05:11 EDT 2021. Contains 343072 sequences. (Running on oeis4.)