The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A010209 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A010209

Continued fraction for sqrt(160).
(history; published version)

#27 by Michael De Vlieger at Wed Nov 22 08:31:43 EST 2023

STATUS

reviewed

approved

#26 by Michel Marcus at Wed Nov 22 00:33:15 EST 2023

STATUS

proposed

reviewed

#25 by Amiram Eldar at Wed Nov 22 00:19:32 EST 2023

STATUS

editing

proposed

#24 by Amiram Eldar at Wed Nov 22 00:03:00 EST 2023

FORMULA

From Amiram Eldar, Nov 22 2023: (Start)

Multiplicative with a(2) = 1, a(4) = 5, a(2^e) = 24 for e >= 3, and a(p^e) = 1 for an odd prime p.

Dirichlet g.f.: zeta(s) * (1 + 1/4^(s-1) + 19/8^s). (End)

#23 by Amiram Eldar at Wed Nov 22 00:02:48 EST 2023

LINKS

G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">Contfrac</a>.

<a href="/index/Con#confC">Index entries for continued fractions for constants</a>.

<a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 1).

FORMULA

a(n) = (1/32)*(-87*(n mod 8) + 5*((n+1) mod 8) + 5*((n+2) mod 8) + 21*((n+3) mod 8) - 11*((n+4) mod 8) + 5*((n+5) mod 8) + 5*((n+6) mod 8) + 97*((n+7) mod 8)) - 12*(C(2*n,n) mod 2), with n >= 0. - Paolo P. Lava, Jul 28 2009

KEYWORD

nonn,cofr,easy,mult

STATUS

approved

editing

#22 by Susanna Cuyler at Sun Jul 15 22:01:29 EDT 2018

STATUS

reviewed

approved

#21 by Michel Marcus at Sun Jul 15 13:18:20 EDT 2018

STATUS

proposed

reviewed

#20 by Jon E. Schoenfield at Sun Jul 15 12:51:01 EDT 2018

STATUS

editing

proposed

#19 by Jon E. Schoenfield at Sun Jul 15 12:50:58 EDT 2018

FORMULA

a(n) = (1/32)*{(-87*(n mod 8) + 5*[((n+1) mod 8]) + 5*[((n+2) mod 8]) + 21*[((n+3) mod 8]) - 11*[((n+4) mod 8]) + 5*[((n+5) mod 8]) + 5*[((n+6) mod 8]) + 97*[((n+7) mod 8]})) - 12*[(C(2*n,n) mod 2], ), with n >= 0 [From _. - _Paolo P. Lava_, Jul 28 2009]

MATHEMATICA

ContinuedFraction[Sqrt[160], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 23 2011 *)

AUTHOR

N. J. A. Sloane.

STATUS

approved

editing

#18 by Ray Chandler at Thu Mar 09 16:29:14 EST 2017

STATUS

editing

approved