A041265 -id:A041265 - cp's OEIS frontend

A040132 Continued fraction for sqrt(145).

12, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24

Offset: 0

N. J. A. Sloane

			12 + 1/(24 + 1/(24 + 1/(24 + 1/(24 + ...)))) = sqrt(145).

Cf. A041264/A041265 (convergents), A176910 (decimal expansion).

Cf. A040000, A040002, A040006.

Digits := 100: convert(evalf(sqrt(N)),confrac,90,'cvgts'):

ContinuedFraction[Sqrt[145],300] (* Vladimir Joseph Stephan Orlovsky, Mar 13 2011*)

From Elmo R. Oliveira, Feb 12 2024: (Start)
a(n) = 24 for n >= 1.
G.f.: 12*(1+x)/(1-x).
E.g.f.: 24*exp(x) - 12.
a(n) = 12*A040000(n) = 6*A040002(n) = 4*A040006(n). (End)

A041264 Numerators of continued fraction convergents to sqrt(145).

Original entry on oeis.org

12, 289, 6948, 167041, 4015932, 96549409, 2321201748, 55805391361, 1341650594412, 32255419657249, 775471722368388, 18643576756498561, 448221313878333852, 10775955109836511009, 259071143949954598068, 6228483409908746864641, 149742672981759879349452

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (24,1).

Cf. A041265.

Numerator[Convergents[Sqrt[145], 30]] (* Vincenzo Librandi, Oct 31 2013 *)

a(n) = 24*a(n-1)+a(n-2) for n>1; a(0)=12, a(1)=289. G.f.: (12+x)/(1-24*x-x^2). [Philippe Deléham, Nov 21 2008]

More terms from Colin Barker, Nov 06 2013

cp's OEIS Frontend

A040132 Continued fraction for sqrt(145).

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