login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
KEYWORD
nonn
AUTHOR
Wolfdieter Lang, Nov 29 2002
EXTENSIONS
More terms from Max Alekseyev, Mar 03 2010
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 21 12:56 EDT 2024. Contains 371870 sequences. (Running on oeis4.)