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%I A010701 #108 Oct 29 2024 12:20:51
%S A010701 3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,
%T A010701 3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,
%U A010701 3,3,3,3,3,3,3,3,3,3,3,3,3
%N A010701 Constant sequence: the all 3's sequence.
%C A010701 Decimal expansion of 1/3. - _Raymond Wang_, Mar 06 2010
%C A010701 Continued fraction expansion of (3+sqrt(13))/2. - _Bruno Berselli_, Mar 15 2011
%H A010701 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>.
%H A010701 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=1011">Encyclopedia of Combinatorial Structures 1011</a>.
%H A010701 Daniele A. Gewurz and Francesca Merola, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL6/Gewurz/gewurz5.html">Sequences realized as Parker vectors of oligomorphic permutation groups</a>, J. Integer Seqs., Vol. 6 (2003), Article 03.1.6.
%H A010701 Rick Mabry, <a href="https://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/proof-without-words-14-142-143-ldots-13">Proof without words: 1/4+(1/4)^2+(1/4)^3+...=1/3</a>, Math. Mag., Vol. 72, No. 1 (1999), p. 63.
%H A010701 Dominika Závacká, Cristina Dalfó, and Miquel Angel Fiol, <a href="https://ceur-ws.org/Vol-3792/paper19.pdf">Integer sequences from k-iterated line digraphs</a>, CEUR: Proc. 24th Conf. Info. Tech. - Appl. and Theory (ITAT 2024) Vol 3792, 156-161. See p. 161, Table 2.
%H A010701 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).
%H A010701 <a href="/index/Di#divseq">Index to divisibility sequences</a>
%F A010701 G.f.: 3/(1-x). - _Bruno Berselli_, Mar 15 2011
%F A010701 E.g.f.: 3*e^x. - _Vincenzo Librandi_, Jan 24 2012
%F A010701 a(n) = A040000(n) + A054977(n). - _Reinhard Zumkeller_, May 06 2012
%F A010701 a(n) = 3*A000012(n). - _Michel Marcus_, Dec 18 2015
%F A010701 a(n) = floor(1/(n - cot(1/n))). - _Clark Kimberling_, Mar 10 2020
%F A010701 Equals Sum_{k>=1} (1/4)^k (as a constant). - _Michel Marcus_, Jun 11 2020
%F A010701 Equals Sum_{k>=2} (k-1)/binomial(2*k,k) (as a constant). - _Amiram Eldar_, Jun 05 2021
%F A010701 Equals Sum_{k>=1} (-1)^(k+1)/2^k. - _Michal Paulovic_, Mar 02 2023
%e A010701 1/3 = 0.33333333333333333333333333333333333333333333... - _Bruno Berselli_, Mar 21 2014
%p A010701 evalf(1/3, 100); # _Michal Paulovic_, Mar 02 2023
%t A010701 Table[3, {100}] (* _Wesley Ivan Hurt_, Jul 16 2014 *)
%o A010701 (Haskell)
%o A010701 a010701 = const 3
%o A010701 a010701_list = repeat 3  -- _Reinhard Zumkeller_, May 07 2012
%o A010701 (Maxima) makelist(3, n, 0, 30); /* _Martin Ettl_, Nov 09 2012 */
%o A010701 (PARI) a(n)=3 \\ _Felix Fröhlich_, Jul 16 2014
%o A010701 (Python)
%o A010701 def A010701(n): return 3 # _Chai Wah Wu_, Nov 10 2022
%Y A010701 Cf. A000012, A040000, A054977.
%K A010701 nonn,cons,easy
%O A010701 0,1
%A A010701 _N. J. A. Sloane_

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