The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A040756 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A040756

Continued fraction for sqrt(785).
(history; published version)

#21 by Peter Luschny at Fri Feb 16 11:27:43 EST 2024

STATUS

reviewed

approved

#20 by Michel Marcus at Fri Feb 16 10:16:50 EST 2024

STATUS

proposed

reviewed

#19 by Elmo R. Oliveira at Fri Feb 16 06:36:23 EST 2024

STATUS

editing

proposed

#18 by Elmo R. Oliveira at Fri Feb 16 06:27:04 EST 2024

FORMULA

From Elmo R. Oliveira, Feb 16 2024: (Start)

a(n) = 56 for n >= 1.

G.f.: 28*(1+x)/(1-x).

E.g.f.: 56*exp(x) - 28.

a(n) = 28*A040000(n) = 14*A040002(n) = 7*A040012(n). (End)

EXAMPLE

28 + 1/(56 + 1/(56 + 1/(56 + 1/(56 + ...)))) = sqrt(785).

CROSSREFS

Cf. A042512/A042513 (convergents).

Cf. A040000, A040002, A040012.

AUTHOR

N. J. A. Sloane.

STATUS

approved

editing

#17 by Joerg Arndt at Wed Dec 27 00:23:26 EST 2023

STATUS

editing

approved

#16 by Joerg Arndt at Wed Dec 27 00:23:24 EST 2023

FORMULA

a(n)=56-28*[C(2*n,n) mod 2], with n>=0 [From Paolo P. Lava, May 20 2009]

STATUS

approved

editing

#15 by Ray Chandler at Fri Mar 10 16:06:33 EST 2017

STATUS

editing

approved

#14 by Ray Chandler at Fri Mar 10 16:06:29 EST 2017

LINKS

<a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).

STATUS

approved

editing

#13 by Charles R Greathouse IV at Thu Nov 21 12:46:48 EST 2013

MATHEMATICA

Block[{$MaxExtraPrecision =1000}, ContinuedFraction[Sqrt[785], 70]] (* or *) PadRight[{28}, 70, 56] (* From _Harvey P. Dale, _, May 09 2012 *)

Discussion

Thu Nov 21

12:46

OEIS Server: https://oeis.org/edit/global/2062

#12 by Harvey P. Dale at Wed May 09 14:15:26 EDT 2012

STATUS

editing

approved