The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A010153 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A010153

Continued fraction for sqrt(75) (or 5*sqrt(3)).
(history; published version)

#34 by Harvey P. Dale at Sat Oct 05 17:44:25 EDT 2024

STATUS

editing

approved

#33 by Harvey P. Dale at Sat Oct 05 17:44:23 EDT 2024

MATHEMATICA

PadRight[{8}, 120, {16, 1, 1, 1}] (* Harvey P. Dale, Oct 05 2024 *)

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approved

editing

#32 by Hugo Pfoertner at Mon Nov 13 07:08:55 EST 2023

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reviewed

approved

#31 by Michel Marcus at Mon Nov 13 01:36:09 EST 2023

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proposed

reviewed

#30 by Amiram Eldar at Mon Nov 13 00:18:19 EST 2023

STATUS

editing

proposed

#29 by Amiram Eldar at Mon Nov 13 00:12:11 EST 2023

FORMULA

a(n) =(1/24)*{-71*(n mod 4)+19*[(n+1) mod 4]+19*[(n+2) mod 4]+109*[(n+3) mod 4]}-8*[C(2*n,n) mod 2], with n>=0. - Paolo P. Lava, Jul 24 2009

#28 by Amiram Eldar at Mon Nov 13 00:11:59 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_04">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 1).

FORMULA

From Amiram Eldar, Nov 13 2023: (Start)

Multiplicative with a(2) = 1, a(2^e) = 16 for e >= 2, and a(p^e) = 1 for an odd prime p.

Dirichlet g.f.: zeta(s) * (1 + 15/4^s). (End)

KEYWORD

nonn,cofr,easy,mult

STATUS

approved

editing

#27 by Susanna Cuyler at Wed Jun 12 19:14:47 EDT 2019

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proposed

approved

#26 by Michel Marcus at Wed Jun 12 12:13:08 EDT 2019

STATUS

editing

proposed

#25 by Michel Marcus at Wed Jun 12 12:13:03 EDT 2019

FORMULA

a(n) =(1/24)*{-71*(n mod 4)+19*[(n+1) mod 4]+19*[(n+2) mod 4]+109*[(n+3) mod 4]}-8*[C(2*n,n) mod 2], with n>=0. - Paolo P. Lava, Jul 24 2009

STATUS

approved

editing