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

5, 15, 25, 35, 45, 55, 65, 75, 85, 95, 105, 115, 125, 135, 145, 155, 165, 175, 185, 195, 205, 215, 225, 235, 245, 255, 265, 275, 285, 295, 305, 315, 325, 335, 345, 355, 365, 375, 385, 395, 405, 415, 425, 435, 445, 455, 465, 475, 485, 495, 505, 515, 525, 535

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Continued fraction expansion of tanh(1/5). - Benoit Cloitre, Dec 17 2002

n such that 5 divides the numerator of B(2n) where B(2n) = the 2n-th Bernoulli number. - Benoit Cloitre, Jan 01 2004

5 times odd numbers. - Omar E. Pol, May 02 2008

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

Successive sums: 5, 20, 45, 80, 125, ... (see A033429). - Philippe Deléham, Dec 08 2011

3^a(n) + 1 is divisible by 61. - Vincenzo Librandi, Feb 05 2013

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

References

• A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 189. - From N. J. A. Sloane, Dec 01 2012

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Tanya Khovanova, Recursive Sequences.
• Index to sequences related to polygonal numbers.
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A000367, A002193, A016957, A057145, A094884, A139600, A139606, A182007.

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

Cf. A005408, A008587, A033429, A267541, A323288.

Programs

Haskell

a017329 = (+ 5) . (* 10)
a017329_list = [5, 15 ..]  -- Reinhard Zumkeller, Apr 10 2015

Magma

[10*n + 5: n in [0..60]]; // Vincenzo Librandi, Feb 05 2013

Mathematica

Range[5, 1000, 10] (* Vladimir Joseph Stephan Orlovsky, May 28 2011 *)
LinearRecurrence[{2,-1},{5,15},60] (* Harvey P. Dale, Nov 16 2019 *)

PARI

a(n)=10*n+5 \\ Charles R Greathouse IV, Sep 24 2015

Formula

a(n) = 5*A005408(n). - Omar E. Pol, Oct 19 2008

a(n) = 20*n - a(n-1) (with a(0)=5). - Vincenzo Librandi, Nov 19 2010

G.f.: 5*(x+1)/(x-1)^2. - Colin Barker, Nov 14 2012

a(n) = A057145(n+2,5). - R. J. Mathar, Jul 28 2016

E.g.f.: 5*exp(x)*(1 + 2*x). - Stefano Spezia, Feb 14 2020

Sum_{n>=0} (-1)^n/a(n) = Pi/20. - Amiram Eldar, Dec 12 2021

From Amiram Eldar, Nov 23 2024: (Start)

Product_{n>=0} (1 - (-1)^n/a(n)) = sqrt(5-sqrt(5))/2 = sqrt(2)*sin(Pi/5) = A182007/A002193.

Product_{n>=0} (1 + (-1)^n/a(n)) = phi/sqrt(2) (A094884). (End)

a(n) = (n+3)^2 - (n-2)^2. - Alexander Yutkin, Mar 16 2025

From Elmo R. Oliveira, Apr 12 2025: (Start)

a(n) = 2*a(n-1) - a(n-2).

a(n) = A008587(2*n+1). (End)