The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A041014

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A041014

Numerators of continued fraction convergents to sqrt(11).
(history; published version)

#30 by Amiram Eldar at Mon Jun 19 04:24:25 EDT 2023

STATUS

reviewed

approved

#29 by Michel Marcus at Mon Jun 19 02:25:47 EDT 2023

STATUS

proposed

reviewed

#28 by Jon E. Schoenfield at Mon Jun 19 02:04:43 EDT 2023

STATUS

editing

proposed

#27 by Jon E. Schoenfield at Mon Jun 19 02:04:40 EDT 2023

FORMULA

G.f.: (3 + 10*x + 3*x^2 - x^3)/(1 - 20*x^2 + x^4).

MATHEMATICA

Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[11], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 16 2011 *)

AUTHOR

N. J. A. Sloane.

STATUS

approved

editing

#26 by Susanna Cuyler at Fri Nov 01 22:20:13 EDT 2019

STATUS

proposed

approved

#25 by M. F. Hasler at Fri Nov 01 21:10:02 EDT 2019

STATUS

editing

proposed

#24 by M. F. Hasler at Fri Nov 01 21:09:57 EDT 2019

LINKS

<a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,20,0,-1).

PROG

(PARI) A041014=contfracpnqn(c=contfrac(sqrt(11)), #c)[1, ][^-1] \\ Discard last element which may be incorrect. Use e.g. \p999 to get more terms, or extend as follows:

{A041014_upto(N, A=Vec(A041014, N))=for(n=#A041014+1, N, A[n]=20*A[n-2]-A[n-4]); A041014=A} \\ M. F. Hasler, Nov 01 2019

CROSSREFS

Cf. A010468, A041015 (denominators).

Analog for other sqrt(m): A001333 (m=2), A002531 (m=3), A001077 (m=5), A041006 (m=6), A041008 (m=7), A041010 (m=8), A005667 (m=10), A041016 (m=12), ..., A042936 (m=1000).

STATUS

approved

editing

#23 by Charles R Greathouse IV at Sat Jun 13 00:49:20 EDT 2015

LINKS

<a href="/index/Rec">Index to sequences with entries for linear recurrences with constant coefficients</a>, signature (0,20,0,-1).

Discussion

Sat Jun 13

00:49

OEIS Server: https://oeis.org/edit/global/2439

#22 by Charles R Greathouse IV at Fri Jun 12 15:23:56 EDT 2015

LINKS

<a href="/index/Rea#recLCCRec">Index to sequences with linear recurrences with constant coefficients</a>, signature (0,20,0,-1).

Discussion

Fri Jun 12

15:23

OEIS Server: https://oeis.org/edit/global/2436

#21 by Charles R Greathouse IV at Sun Aug 03 14:16:24 EDT 2014

MATHEMATICA

Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[11], n]]], {n, 1, 50}] (*From _Vladimir Joseph Stephan Orlovsky, _, Mar 16 2011*)

Discussion

Sun Aug 03

14:16

OEIS Server: https://oeis.org/edit/global/2269