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 A078355 Minimal (positive) solution a(n) of Pell equation b(n)^2 - D(n)*a(n)^2 = +4 with D(n)= A077425(n). The companion sequence is a(n)=A077428(n). 18
 1, 3, 16, 1, 5, 8, 24, 640, 1, 7, 40, 195, 32, 3, 534000, 1, 9, 106000, 3, 12754704, 40, 8, 6525, 226592, 1, 11, 2968, 15, 1039424, 16, 48, 305, 352, 3621, 1856, 1, 13, 9384, 126585, 1360, 8, 896073208080, 56, 72664, 3, 6440, 5, 521904, 1, 15, 140510608, 5 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS For the conversion of the (x,y) values of Perron's table to the (b(n),a(n)) values see a A077428 comment. For the general solution of Pell b^2 - D(n)*a^2 = +4 see a comment in A077428 (with a and b interchanged). 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 S. R. Finch, Class number theory Steven R. Finch, Class number theory [Cached copy, with permission of the author] MATHEMATICA d = Select[Range[5, 300, 4], !IntegerQ[Sqrt[#]]&]; a[n_] := Module[{a, b, r}, b /. {r = Reduce[a > 0 && b > 0 && a^2 - d[[n]]*b^2 == 4, {a, b}, Integers]; (r /. C[1] -> 0) || (r /. C[1] -> 1) // ToRules} // Select[#, IntegerQ, 1] &] // First; Table[a[n], {n, 1, 52}] (* Jean-François Alcover, Jul 30 2013 *) CROSSREFS Sequence in context: A004002 A216149 A194604 * A107823 A139815 A165969 Adjacent sequences: A078352 A078353 A078354 * A078356 A078357 A078358 KEYWORD nonn AUTHOR Wolfdieter Lang, Nov 29 2002 EXTENSIONS More terms from Max Alekseyev, Mar 03 2010 STATUS approved

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Last modified December 5 14:51 EST 2022. Contains 358588 sequences. (Running on oeis4.)