This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A017329 #98 Apr 12 2025 11:20:28
%S A017329 5,15,25,35,45,55,65,75,85,95,105,115,125,135,145,155,165,175,185,195,
%T A017329 205,215,225,235,245,255,265,275,285,295,305,315,325,335,345,355,365,
%U A017329 375,385,395,405,415,425,435,445,455,465,475,485,495,505,515,525,535
%N A017329 a(n) = 10*n + 5.
%C A017329 Continued fraction expansion of tanh(1/5). - _Benoit Cloitre_, Dec 17 2002
%C A017329 n such that 5 divides the numerator of B(2n) where B(2n) = the 2n-th Bernoulli number. - _Benoit Cloitre_, Jan 01 2004
%C A017329 5 times odd numbers. - _Omar E. Pol_, May 02 2008
%C A017329 5th transversal numbers (or 5-transversal numbers): Numbers of the 5th column of positive numbers in the square array of nonnegative and polygonal numbers A139600. Also, numbers of the 5th column in the square array A057145. - _Omar E. Pol_, May 02 2008
%C A017329 Successive sums: 5, 20, 45, 80, 125, ... (see A033429). - _Philippe Deléham_, Dec 08 2011
%C A017329 3^a(n) + 1 is divisible by 61. - _Vincenzo Librandi_, Feb 05 2013
%C A017329 If the initial 5 is changed to 1, giving 1,15,25,35,45,..., these are values of m such that A323288(m)/m reaches a new record high value. - _N. J. A. Sloane_, Jan 23 2019
%D A017329 A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 189. - From _N. J. A. Sloane_, Dec 01 2012
%H A017329 Vincenzo Librandi, <a href="/A017329/b017329.txt">Table of n, a(n) for n = 0..1000</a>
%H A017329 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>.
%H A017329 <a href="/index/Pol#polygonal_numbers">Index to sequences related to polygonal numbers</a>.
%H A017329 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A017329 a(n) = 5*A005408(n). - _Omar E. Pol_, Oct 19 2008
%F A017329 a(n) = 20*n - a(n-1) (with a(0)=5). - _Vincenzo Librandi_, Nov 19 2010
%F A017329 G.f.: 5*(x+1)/(x-1)^2. - _Colin Barker_, Nov 14 2012
%F A017329 a(n) = A057145(n+2,5). - _R. J. Mathar_, Jul 28 2016
%F A017329 E.g.f.: 5*exp(x)*(1 + 2*x). - _Stefano Spezia_, Feb 14 2020
%F A017329 Sum_{n>=0} (-1)^n/a(n) = Pi/20. - _Amiram Eldar_, Dec 12 2021
%F A017329 From _Amiram Eldar_, Nov 23 2024: (Start)
%F A017329 Product_{n>=0} (1 - (-1)^n/a(n)) = sqrt(5-sqrt(5))/2 = sqrt(2)*sin(Pi/5) = A182007/A002193.
%F A017329 Product_{n>=0} (1 + (-1)^n/a(n)) = phi/sqrt(2) (A094884). (End)
%F A017329 a(n) = (n+3)^2 - (n-2)^2. - _Alexander Yutkin_, Mar 16 2025
%F A017329 From _Elmo R. Oliveira_, Apr 12 2025: (Start)
%F A017329 a(n) = 2*a(n-1) - a(n-2).
%F A017329 a(n) = A008587(2*n+1). (End)
%t A017329 Range[5, 1000, 10] (* _Vladimir Joseph Stephan Orlovsky_, May 28 2011 *)
%t A017329 LinearRecurrence[{2,-1},{5,15},60] (* _Harvey P. Dale_, Nov 16 2019 *)
%o A017329 (Magma) [10*n + 5: n in [0..60]]; // _Vincenzo Librandi_, Feb 05 2013
%o A017329 (Haskell)
%o A017329 a017329 = (+ 5) . (* 10)
%o A017329 a017329_list = [5, 15 ..] -- _Reinhard Zumkeller_, Apr 10 2015
%o A017329 (PARI) a(n)=10*n+5 \\ _Charles R Greathouse IV_, Sep 24 2015
%Y A017329 Cf. A000367, A002193, A016957, A057145, A094884, A139600, A139606, A182007.
%Y A017329 Subsequence of A034709, together with A017281, A017293, A139222, A139245, A139249, A139264, A139279 and A139280.
%Y A017329 Cf. A005408, A008587, A033429, A267541, A323288.
%K A017329 nonn,easy
%O A017329 0,1
%A A017329 _N. J. A. Sloane_