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A017329 a(n) = 10*n + 5. 53

%I #86 Sep 08 2022 08:44:42

%S 5,15,25,35,45,55,65,75,85,95,105,115,125,135,145,155,165,175,185,195,

%T 205,215,225,235,245,255,265,275,285,295,305,315,325,335,345,355,365,

%U 375,385,395,405,415,425,435,445,455,465,475,485,495,505,515,525,535

%N a(n) = 10*n + 5.

%C Continued fraction expansion of tanh(1/5). - _Benoit Cloitre_, Dec 17 2002

%C n such that 5 divides the numerator of B(2n) where B(2n) = the 2n-th Bernoulli number. - _Benoit Cloitre_, Jan 01 2004

%C 5 times odd numbers. - _Omar E. Pol_, May 02 2008

%C 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 Successive sums: 5, 20, 45, 80, 125, ... (see A033429). - _Philippe Deléham_, Dec 08 2011

%C 3^a(n) + 1 is divisible by 61. - _Vincenzo Librandi_, Feb 05 2013

%C 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 A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 189. - From _N. J. A. Sloane_, Dec 01 2012

%H Vincenzo Librandi, <a href="/A017329/b017329.txt">Table of n, a(n) for n = 0..1000</a>

%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>.

%H <a href="/index/Pol#polygonal_numbers">Index to sequences related to polygonal numbers</a>.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F a(n) = A005408(n)*5. - _Omar E. Pol_, Oct 19 2008

%F a(n) = 20*n - a(n-1) (with a(0)=5). - _Vincenzo Librandi_, Nov 19 2010

%F G.f.: 5*(x+1)/(x-1)^2. - _Colin Barker_, Nov 14 2012

%F a(n) = A057145(n+2,5). - _R. J. Mathar_, Jul 28 2016

%F E.g.f.: 5*exp(x)*(1 + 2*x). - _Stefano Spezia_, Feb 14 2020

%F Sum_{n>=0} (-1)^n/a(n) = Pi/20. - _Amiram Eldar_, Dec 12 2021

%t Range[5, 1000, 10] (* _Vladimir Joseph Stephan Orlovsky_, May 28 2011 *)

%t LinearRecurrence[{2,-1},{5,15},60] (* _Harvey P. Dale_, Nov 16 2019 *)

%o (Magma) [10*n + 5: n in [0..60]]; // _Vincenzo Librandi_, Feb 05 2013

%o (Haskell)

%o a017329 = (+ 5) . (* 10)

%o a017329_list = [5, 15 ..] -- _Reinhard Zumkeller_, Apr 10 2015

%o (PARI) a(n)=10*n+5 \\ _Charles R Greathouse IV_, Sep 24 2015

%Y Cf. A000367, A016957, A057145, A139600, A139606.

%Y Subsequence of A034709, together with A017281, A017293, A139222, A139245, A139249, A139264, A139279 and A139280.

%Y Cf. also A005408, A267541, A323288.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_

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Last modified March 19 06:32 EDT 2024. Contains 370953 sequences. (Running on oeis4.)