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

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
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

Table of n, a(n) for n=1..52.

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

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