OFFSET
0,1
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 entries for linear recurrences with constant coefficients, signature (2,-1).
FORMULA
a(n) = A005408(n)*5. - 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)) = phi/sqrt(2) (A094884). (End)
MATHEMATICA
Range[5, 1000, 10] (* Vladimir Joseph Stephan Orlovsky, May 28 2011 *)
LinearRecurrence[{2, -1}, {5, 15}, 60] (* Harvey P. Dale, Nov 16 2019 *)
PROG
(Magma) [10*n + 5: n in [0..60]]; // Vincenzo Librandi, Feb 05 2013
(Haskell)
a017329 = (+ 5) . (* 10)
a017329_list = [5, 15 ..] -- Reinhard Zumkeller, Apr 10 2015
(PARI) a(n)=10*n+5 \\ Charles R Greathouse IV, Sep 24 2015
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
STATUS
approved